{"id":14769,"date":"2024-01-02T07:33:00","date_gmt":"2024-01-02T02:03:00","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=14769"},"modified":"2024-01-03T10:16:16","modified_gmt":"2024-01-03T04:46:16","slug":"envision-math-common-core-grade-7-answer-key-topic-3","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-7-answer-key-topic-3\/","title":{"rendered":"enVision Math Common Core Grade 7 Answer Key Topic 3 Analyze And Solve Percent Problems"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 7 Answer Key<\/a>\u00a0Topic 3 Analyze And Solve Percent Problems<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 7th Grade Answers Key Topic 3 Analyze And Solve Percent Problems<\/h2>\n

Topic 3 Essential Question<\/h3>\n

How can percents show proportional relationships between quantities and be used to solve problems?<\/p>\n

3-ACT MATH<\/strong><\/p>\n

\"Envision
\nThe Smart Shopper
\nWhy do stores and manufacturers print coupons? It seems like they lose money every time you use one. Well, some coupons are designed to steer you toward a specific brand and gain your loyalty. Stores also offer coupons to get you into the store, counting on you buying other items while you are there. If you’re clever, you can use multiple coupons. Think about this during the 3-Act Mathematical Modeling lesson.3
\n\"Envision<\/p>\n

Topic 3 enVision STEM Project<\/h3>\n

Did You Know?
\nOne of the first popular activity trackers was a pedometer, which measures number of steps taken. Some sources trace the history of the pedometer back to Leonardo da Vinci.
\n\"Envision
\nA pedometer called Manpo-kei (10,000 steps meter) was introduced in Japan in the mid1960s. Research led by Dr. Yoshiro Hatano indicated that 10,000 steps a day is the ideal energy output to maintain health.
\n\"Envision
\nToday, most activity trackers are electronic devices that can sync to a computer or a smartphone.<\/p>\n

Many activity trackers are wearable technology. Some common places to wear activity trackers are on the wrist, arm, or chest. There are even collar-mounted activity trackers for dogs.
\n\"Envision
\nYour Task: Analyze Activity Tracker Data
\nActivity trackers, also called fitness trackers, have become quite popular in recent years. But is the data collected actually helpful to the user? You and your classmates will explore the types of data that an activity tracker collects, and how that data can help users reach their activity and fitness goals.
\n\"Envision<\/p>\n

Topic 3 GET READY!<\/h3>\n

Review What You Know!<\/strong><\/p>\n

Vocabulary
\n<\/strong>Choose the best term from the box. Write it on the blank.<\/p>\n

    \n
  • percent<\/li>\n
  • proportion<\/li>\n
  • rate<\/li>\n
  • ratio<\/li>\n<\/ul>\n

    Question 1.
    \nA ________is a ratio in which the first term is compared to 100.<\/p>\n

    Answer:
    \nA percent is a ratio in which the first term is compared to 100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA percent is a ratio in which the first term is compared to 100.
    \nfor example:
    \n38\/100 = x\/100.
    \nx = 38%.
    \n38\/100 = 38.<\/p>\n

    \"Analyze<\/p>\n

    Question 2.
    \nA ratio that relates two quantities with different units of measure is a _________.<\/p>\n

    Answer:
    \nA ratio that relates two quantities with different units of measure is a rate.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA ratio that relates two quantities with different units of measure is a rate.
    \nfor example:
    \n34mi\/2 gal.
    \nwe can convert any rate to a unit rate.<\/p>\n

    Question 3.
    \nA statement that two ratios are equal is called a _________.<\/p>\n

    Answer:
    \nA statement that two ratios are equal is called a proportion.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA statement that two ratios are equal is called a proportion.
    \nfor example:
    \n5\/10 = 1\/2.<\/p>\n

    Question 4.
    \nThe relationship “3 students out of 5 students” is an example of a _________.<\/p>\n

    Answer:
    \nThe relationship “3 students out of 5 students” is an example of a ratio.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe relationship “3 students out of 5 students” is an example of a ratio.<\/p>\n

    Fractions, Decimals, and Percents<\/strong><\/p>\n

    Write each number in two equivalent forms as a fraction, decimal, or percent.
    \nQuestion 5.
    \n0.29<\/p>\n

    Answer:
    \nThe number infraction is 29\/100.
    \ndecimal = 0.29.
    \npercent = 29%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number is 0.29.
    \ndecimal = 0.29.
    \npercent = 29%.
    \nfraction = 29\/100.<\/p>\n

    Question 6.
    \n35%<\/p>\n

    Answer:
    \nThe number of fraction is 35\/100.
    \ndecimal = 0.35.
    \npercent = 35%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number is 35%.
    \ndecimal = 0.35.
    \npercent = 35%.
    \nfraction = 35\/100.<\/p>\n

    Question 7.
    \n\\(\\frac{2}{5}\\)<\/p>\n

    Answer:
    \nThe number infraction is 2\/5.
    \ndecimal = 40.0..
    \npercent = 0.4%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number is 2\/5.
    \ndecimal = 40.0.
    \npercent = 0.4%.
    \nfraction = 2\/5.<\/p>\n

    \"Analyze<\/p>\n

    Proportions<\/strong><\/p>\n

    Find the unknown number in each proportion.
    \nQuestion 8.
    \n\\(\\frac{x \\text { days }}{4 \\text { years }}=\\frac{365.25 \\text { days }}{1 \\text { year }}\\)<\/p>\n

    Answer:
    \nx = 1461.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nx\/4 = 365.25.
    \nx = 365.25 x 4.
    \nx = 1461.<\/p>\n

    Question 9.
    \n\\(\\frac{33,264 \\text { feet }}{x \\text { miles }}=\\frac{5,280 \\text { feet }}{1 \\text { mile }}\\)<\/p>\n

    Answer:
    \nx = 1.569.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3364\/x = 5280\/1.
    \nx = 5280\/3364.
    \nx = 1.569.<\/p>\n

    Question 10.
    \nA cooking magazine shows a photo of a main dish on the front cover of 5 out of the 12 issues it publishes each year. Write and solve a proportion to determine how many times a photo of a main dish will be on the front cover during the next 5 years.<\/p>\n

    Answer:
    \nThe number of times a photo of a main dish will be on the front cover during the next 5 years = 3 times.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA cooking magazine shows a photo of a main dish on the front cover of 5 out of the 12 issues it publishes each year.
    \n5\/100 x 12.
    \n0.05 x 12.
    \n0.6.
    \n0.6 x 5 = 3.
    \nso the number of times a photo of the main dish will be on the front cover during the next 5 years = 3 times.<\/p>\n

    Language Development<\/strong><\/p>\n

    Fill in the spider map by writing new vocabulary terms on each diagonal and related ideas.
    \n\"Envision<\/p>\n

    Answer:
    \n25\/100 = 0.25.
    \n50\/100 = 0.5.
    \n75\/100 = 0.75.
    \n100\/100 = 1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe percent of all the terms in problem.
    \nthe four terms are 25, 50, 75, and 100.
    \n25\/100 = 0.25.
    \n50\/100 = 0.5.
    \n75\/100 = 0.75.
    \n100\/100 = 1.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Pick A Project<\/strong><\/p>\n

    PROJECT 3A
    \nHow can you make sure you are getting the best deal?
    \nPROJECT: SEARCH FOR BARGAINS
    \n\"Envision<\/p>\n

    Answer:
    \nYes, I am getting the best deal.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthey kept the discount of 50% on summer sale.
    \n50\/100 = 0.5.
    \nso\u00a0 I am getting the best deal.<\/p>\n

    PROJECT 3B
    \nWhat makes a song’s lyrics easy to remember?
    \nPROJECT: WRITE AND PERFORM A CHEER OR A RAP
    \n\"Envision<\/p>\n

    PROJECT 3C
    \nIf you were to play basketball, what strategies would you practice?
    \nPROJECT: ESTIMATE BASKETS
    \n\"Envision<\/p>\n

    PROJECT 3D
    \nWhat are some elements of your favorite app?
    \nPROJECT: DESIGN AN APP ICON
    \n\"Envision<\/p>\n

    Lesson 3.1 Analyze Percents of Numbers<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nJaime’s older brother and his three friends want to split the cost of lunch. They also want to leave a 15%-20% tip. How much should each person pay?
    \nI can… understand, find, and analyze percents of numbers.
    \n\"Envision
    \nReasoning Which line on the receipt will you use to calculate the tip?<\/p>\n

    Answer:
    \nThe amount should each person pay = 30%<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJaime’s older brother and his three friends want to split the cost of lunch.
    \nThey also want to leave a 15%-20% tip.
    \n15\/100 – 20\/100.
    \n50\/100 = 0.5.
    \n20\/100 = 0.2.
    \n0.5 – 0.2 = 0.3.
    \n30\/100.
    \nso the amount should each person pay = 30%.<\/p>\n

    Focus on math practices
    \nReasoning How would the amount each person pays change if the tip is determined before or after the bill is split?<\/p>\n

    Essential Question<\/strong>
    \nHow do percents show the relationship between quantities?<\/p>\n

    Try It!<\/strong><\/p>\n

    Kita’s phone had a fully charged battery. With normal usage, her phone will last 18 hours. How much time is left on Kita’s phone battery with 12% charge remaining?
    \n\"Envision
    \nKita’s phone battery has __________ hours remaining.<\/p>\n

    Answer:
    \nThe time left on Kita’s phone battery with 12% charge remaining = 3 hours.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKita’s phone had a fully charged battery.
    \nWith normal usage, her phone will last 18 hours.
    \n21\/100 = x\/18.
    \n0.21 = x\/18.
    \nx\/18 x 0.21.
    \nx = 3.78.
    \nso the time left on Kita’s phone battery with 12% charge remaining = 3 hours.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze
    \nConvince Me! Why is 51% of a number more than half of the number?<\/p>\n

    \"Analyze<\/p>\n

    Try It!<\/strong><\/p>\n

    a. Find 0.08% of 720.<\/p>\n

    Answer:
    \n0.576.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.08% of 720.
    \n0.08\/100 x 720.
    \n0.0008 x 720 = 0.576.<\/p>\n

    b. Find 162.5% of 200.<\/p>\n

    Answer:
    \n162.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n162.5% of 200.
    \n162.5\/100 x 200.
    \n1.625 x 100 = 162.5.<\/p>\n

    c. Find 0.3% of 60.<\/p>\n

    Answer:
    \n0.18.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.3% of 60.
    \n0.3\/100 x 60.
    \n0.003 x 60 = 0.18.<\/p>\n

    KEY CONCEPT<\/strong>
    \nA percent is one way to represent the relationship between two quantities, generally that of a part to the whole.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question How do percents show the relationship between quantities?<\/p>\n

    Answer:
    \nx = 9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n60\/100 = x\/15.
    \n0.6 = x\/15.
    \n0.6 x 15 = x.
    \nx = 9.<\/p>\n

    Question 2.
    \nReasoning<\/strong> How does a value that is greater than 100% of the original value or less than 1% of the original value compare to the original value?.<\/p>\n

    Answer:
    \nThe original value is greater than 1%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe original value is 9%.
    \n9\/100 = 0.09.
    \n1\/100 = 0.01.
    \n0.01 is greater than 0.09.
    \nso the original value is greater than 1%.<\/p>\n

    Question 3.
    \nConstruct Arguments<\/strong> Gene stated that finding 25% of a number is the same as dividing the number by \\(\\frac{1}{4}\\). Is Gene correct? Explain.<\/p>\n

    Answer:
    \nYes, Gene was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nGene stated that finding 25% of a number is the same as dividing the number by \\(\\frac{1}{4}\\).
    \n25\/100 = 0.25.
    \n1\/4 of 100.
    \nso Gene was correct.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nAn 8-ounce serving of apples contains 8% of your daily vitamin C. How many ounces of apples would you need to get 100% of your daily vitamin C?<\/p>\n

    Answer:
    \nThe number of ounces of apples would you need to get 100% of your daily vitamin C = 100-ounce.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn 8-ounce serving of apples contains 8% of your daily vitamin C.
    \nfor 8-ounce it will get 8%.
    \nfor 100 ounces it will get 100%.
    \nso 100 ounces of apples would you need to get 100% of your daily vitamin C.<\/p>\n

    Question 5.
    \nFind the percent of each number.
    \na. 59% of 640<\/p>\n

    Answer:
    \n377.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n59% of 640.
    \n59\/100 x 640.
    \n0.59 x 640.
    \n377.6.<\/p>\n

    b. 0.20% of 3,542<\/p>\n

    Answer:
    \n7.084.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.20% of 3542.
    \n0.20\/100 x 3542.
    \n0.002 x 3542.
    \n7.084.<\/p>\n

    c. 195% of 568<\/p>\n

    Answer:
    \n1107.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n195% of 568.
    \n195\/100 x 568.
    \n1.95 x 568.
    \n1107.6.<\/p>\n

    d. 74% of 920<\/p>\n

    Answer:
    \n680.8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n74% of 920.
    \n74\/100 x 920.
    \n0.74 x 920.
    \n680.8.<\/p>\n

    Question 6.
    \nWater is 2 parts hydrogen and 1 part oxygen (H2<\/sup>O). For one molecule of water, each atom has the atomic mass unit, u, shown. What percent of the mass of a water molecule is hydrogen?
    \n\"Envision<\/p>\n

    Answer:
    \nThe mass of a water molecule in hydrogen = 2.02.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nWater is 2 parts hydrogen and 1 part oxygen (H2<\/sup>O).
    \nFor one molecule of water, each atom has an atomic mass unit.
    \nthe mass of hydrogen is 1.01.
    \n1.01 x 2 = 2.02.
    \nso the mass of a water molecule in hydrogen is 2.02.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7-8, fill in the boxes to solve.
    \nQuestion 7.
    \nA local Little League has a total of 60 players, 80% of whom are right-handed. How many right-handed players are there?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of right-handed players is there = 48.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA local Little League has a total of 60 players,
    \n80% of whom are right-handed.
    \n80\/100 x 60.
    \n0.8 x 60.
    \n48.
    \nso the number of right-handed players is there = 48.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 8.
    \nSandra’s volleyball team has a total of 20 uniforms. 20% are medium-sized uniforms. How many uniforms are medium-sized?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of uniforms is medium-sized = 4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSandra’s volleyball team has a total of 20 uniforms.
    \n20% are medium-sized uniforms.
    \n20\/100 = 0.20.
    \n0.20 x 20 = 4.
    \nso the number of uniforms are medium-sized = 4.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 9.
    \nMeg is a veterinarian. In a given week, 50% of the 16 dogs she saw were Boxers. Steve is also a veterinarian. In the same week, 7 of the 35 dogs he saw this week were Boxers. Each wants to record the part, the whole, and the percent.
    \na. Does Meg need to find the part, the whole, or the percent?<\/p>\n

    Answer:
    \nMeg needs to find the whole = 8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMeg is a veterinarian. In a given week, 50% of the 16 dogs she saw were boxers.
    \nSteve is also a veterinarian.
    \nIn the same week, 7 of the 35 dogs he saw this week were Boxers.
    \n50\/100 x 16.
    \n0.5 x 16 = 8.
    \n7\/35 x 100.
    \n0.2 x 100 = 20.<\/p>\n

    b. Does Steve need to find the part, the whole, or the percent?<\/p>\n

    Answer:
    \nSteve needs to find the part.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSteve is also a veterinarian.
    \nIn the same week, 7 of the 35 dogs he saw this week were Boxers.
    \n50\/100 x 16.
    \n0.5 x 16 = 8.
    \n7\/35 x 100.
    \n0.2 x 100 = 20.
    \nso steve needs to find the part.<\/p>\n

    Question 10.
    \nOlivia is a stockbroker. She makes 4% of her sales in commission. Last week, she sold $7,200 worth of stocks.
    \na. How much commission did she make last week?<\/p>\n

    Answer:
    \nThe much commission did she make last week = $288.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOlivia is a stockbroker.
    \nShe makes 4% of her sales in commission.
    \nLast week, she sold $7,200 worth of stocks.
    \n4\/100 x 7200.
    \n0.04 x 7200 = 288.
    \nso the much commission did she make last week = $288.<\/p>\n

    b. If she were to average that same commission each week, how much would she make in commissions in a year, treating a year as having exactly 52 weeks?<\/p>\n

    Answer:
    \nThe much would she make in commissions in a year, treating a year as having exactly 52 weeks = $3744.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIf she were to average that same commission each week.
    \n52\/100 = 0.52.
    \n0.52 x 7200 = 3744.
    \nso the much she make in commission is $3744.<\/p>\n

    Question 11.
    \nThe registration fee for a used car is 0.8% of the sale price of $5,700. How much is the fee?<\/p>\n

    Answer:
    \nThe fee is $45.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe registration fee for a used car is 0.8% of the sale price of $5,700.
    \n0.8\/100 x 5700.
    \n0.008 x 5700.
    \n45.6.
    \nso the fee is $45.6.<\/p>\n

    Question 12.
    \nThe total cost of an item is the price plus the sales tax.
    \nFind the sales tax to complete the table. Then find the total cost of the item.
    \n\"Envision<\/p>\n

    Answer:
    \nThe total cost of the item = $1.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe total cost of an item is the price plus the sales tax.
    \n4\/100 x 40.
    \n0.04 x 40.
    \n1.6.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 13.
    \nIs 700% of 5 less than 10, greater than 10 but less than 100, or greater than 100? Explain your reasoning.<\/p>\n

    Answer:
    \n35 is greater than 10 but less than 100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n700\/100 x 5.
    \n7 x 5.
    \n35.
    \n35 is greater than 10 but less than 100.<\/p>\n

    Question 14.
    \nIs 250% of 44 less than 100, greater than 100 but less than 150, or greater than 150? Explain your reasoning.<\/p>\n

    Answer:
    \n110 is greater than 100 but less than 150.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n250% of 44.
    \n250\/100 x 44.
    \n2.5 x 44.
    \n110.<\/p>\n

    Question 15.
    \nThe seed and skin of a typical avocado is about 30%-40% of the avocado’s weight. For an 8-ounce avocado, how many ounces of edible fruit does it have?<\/p>\n

    Answer:
    \nThe number of ounces of edible fruit does it have = 5.6 ounces.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe seed and skin of a typical avocado is about 30%-40% of the avocado’s weight.
    \n30\/100 – 40\/100.
    \n30 + 40 = 70.
    \n70\/100 = 0.7.
    \n0.7 x 8 = 5.6.
    \nso the number of ounces of edible fruit does it have = 5.6 ounces.<\/p>\n

    Question 16.
    \nA new health drink has 130% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 45 mg. How many milligrams of the vitamin are in the drink?<\/p>\n

    Answer:
    \nThe milligrams of the vitamin is in the drink = 60.75 mg.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA new health drink has 130% of the recommended daily allowance (RDA) for a certain vitamin.
    \nThe RDA for this vitamin is 45 mg.
    \n135\/100 x 45.
    \n1.35 x 45.
    \n60.75.
    \nso the milligrams of the vitamin is in the drink = 60.75 mg.<\/p>\n

    Question 17.
    \nMake Sense and Persevere 153 is 0.9% of what number? Tell which equivalent ratios you used to find the solution.<\/p>\n

    Answer:
    \nThe equivalent ratios used to find the solution = 1.377.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n153 is 0.9%.
    \n153 x 0.9\/100.
    \n153 x 0.009.
    \n1.377.
    \nso the equivalent ratio used to find the solution is 1.377.<\/p>\n

    Question 18.
    \nConstruct Arguments<\/strong> Brad says that if a second number is 125% of the first number, then the first number must be 75% of the second number. Is he correct? Justify your answer.<\/p>\n

    Answer:
    \nYes, Brad was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nBrad says that if a second number is 125% of the first number.
    \nthe first number must be 75%of the second number.
    \n125\/100 = 1.25.
    \n75\/100 = 0.75.
    \nso he was correct.<\/p>\n

    Question 19.
    \nHigher-Order Thinking<\/strong> Mark and Joe work as jewelers. Mark has an hourly wage of $24 and gets overtime for every hour he works over 40 hours. The overtime pay rate is 150% of the normal rate. Joe makes 5% commission on all jewelry he sells. Who earns more money in a week if Mark works 60 hours and Joe sells $21,000 worth of jewelry? Explain.<\/p>\n

    Answer:
    \nJoe earns more money than the mark.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMark and Joe work as jewelers.
    \nMark has an hourly wage of $24 and gets overtime for every hour he works over 40 hours.
    \nThe overtime pay rate is 150% of the normal rate.
    \n5\/100 = 0.05.
    \n40 x 60 = 2400.
    \nso Joe earns more money than the mark.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 20.
    \nPamela and John work as tutors at two different test-prep companies. Pamela earns $20 per hour. John earns $65 per pupil. Pamela works 40 hours each week. John has 11 pupils. Who earns more money in a week? Explain.<\/p>\n

    Answer:
    \nThe more money earns in a week = Pamela.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPamela and John work as tutors at two different test-prep companies.
    \nPamela earns $20 per hour.
    \nJohn earns $65 per pupil.
    \nPamela works 40 hours each week.
    \nJohn has 11 pupils.
    \n40 x $20 = $800.
    \n$65 x 11 = $715.
    \nso pamela earns more than john.<\/p>\n

    Question 21.
    \nAn Olympic-sized pool, which holds 660,000 gallons of water, is only 63% full. The pool maintenance company adds more water, filling the pool to 90% full. How many gallons of water did they add?
    \nA. 244,200
    \nB. 594,000
    \nC. 178,200
    \nD. 415,800<\/p>\n

    Answer:
    \nThe number of gallons of water they add = 178,200 gallons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn Olympic-sized pool, which holds 660,000 gallons of water, is only 63% full.
    \nThe pool maintenance company adds more water, filling the pool to 90% full.
    \n63 – 90 = 27.
    \n27 x 660,000 = 178,200.<\/p>\n

    Lesson 3.2 Connect Percent and Proportion<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nA florist is making flower arrangements for a party. He uses purple and white flowers in a ratio of 3 purple flowers to 1 white flower. How many flowers will he need in order to make 30 identical arrangements?
    \nI can… use proportions to solve percent problems.
    \n\"Envision<\/p>\n

    Look for Relationships
    \nHow are the number of purple flowers related to the number of white flowers?<\/p>\n

    Answer:
    \nThe ratio of purple flowers to the number of white flowers = 1: 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA florist is making flower arrangements for a party.
    \nHe uses purple and white flowers in a ratio of 3 purple flowers to 1 white flower.
    \nthe ratio is 1 : 3.
    \nso the ratio of purple flowers to the number of white flowers = 1: 3.<\/p>\n

    Focus on math practices
    \nMake Sense and Persevere If the florist can only buy white flowers in groups of flowers that have 3 white flowers and 2 red flowers, how many red flowers will the florist have to purchase? Explain your answer.<\/p>\n

    Answer:
    \nThe ratio of white flowers to the number of red flowers = 12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIf the florist can only buy white flowers in groups of flowers that have 3 white flowers and 2 red flowers.
    \n2 + 3 = 5.
    \n5 x 6 = 30.
    \n2 + 2 + 2 + 2 + 2 = 12.
    \nso the ratio of white flowers to the number of red flowers = 12.<\/p>\n

    Essential Question<\/strong>
    \nHow does proportional reasoning relate to percent?<\/p>\n

    Try It!<\/strong><\/p>\n

    Camila makes 2 of her 5 shots attempted. Is the percent of shots she made more than, less than, or the same as Emily’s percent of shots?
    \n\"Envision
    \nCamila made _______% of her shots.
    \nCamila’s percent of the shots made is _______ Emily’s.<\/p>\n

    Answer:
    \nCamila made 2\/5% of her shots.
    \nCamila’s percent of the sots made is 40 Emily’s.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCamila makes 2 of her 5 shots attempted.
    \n2\/5 = p\/100.
    \np = 2\/5 x 100.
    \np = 0.4 x 100.
    \np = 40.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Convince Me! A hockey goalie stops 37 out of 40 shots. What percent of attempted goals did she stop?<\/p>\n

    Answer:
    \nThe percent of attempted goals did she stop = 14.8%<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA hockey goalie stops 37 out of 40 shots.
    \n37\/100 x 40.
    \n0.37 x 40.
    \n14.8 %.
    \nso the percent of attempted goals did she stop = 14.8%.<\/p>\n

    Try It!<\/strong><\/p>\n

    a. Megan’s room is expanded so the width is 150% of 3 meters. What is the new width?<\/p>\n

    Answer:
    \nThe new width = 4.5 meters.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \nMegan’s room is expanded so the width is 150% of 3 meters.
    \n150\/100 x 3.
    \n15\/10 x 3.
    \n1.5 x 3.
    \n4.5 meters.<\/p>\n

    b. Use the soy milk label in Example 3. What is the recommended amount of iron needed each day? Round your answer to the nearest mg.<\/p>\n

    Answer:
    \nThe recommended amount of iron needed each day =<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,<\/p>\n

    KEY CONCEPT<\/strong>
    \nPercent problems represent a kind of proportional relationship. You can use proportional reasoning to solve percent problems.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How does proportional reasoning relate to percent?<\/p>\n

    Answer:
    \npart\/whole = p\/100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPercent problems represent a kind of proportional relationship.
    \nif the whole is 100%.
    \npart is p.
    \npart\/whole = p\/100.<\/p>\n

    Question 2.
    \nReasoning<\/strong> Why does one of the ratios in a percent proportion always have a denominator of 100?<\/p>\n

    Answer:
    \nThe proportion always has a denominator of 100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe whole is always 100%.
    \nso part \/whole = p\/100.
    \nso the proportion always has a denominator of 100.<\/p>\n

    Question 3.
    \nConstruct Arguments<\/strong> The proportion \\(\\frac{75}{W}=\\frac{150}{100}\\) can be used to find the whole, w. Use the language of percent to explain whether w is less than or greater than 75.<\/p>\n

    Answer:
    \nThe weight is greater than 75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe proportion \\(\\frac{75}{W}=\\frac{150}{100}\\) can be used to find the whole, w.
    \n75\/w = 150\/100.
    \n75\/w = 1.5.
    \nw = 1.5 x 75.
    \nw = 112.5.
    \nthe weight is greater than 75.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nWrite a percent proportion for the bar diagram shown.
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent proportion for the bar diagram is 11.56<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n68\/100 = 17\/p.
    \n0.68 = 17\/p.
    \n0.68 x 17 = p.
    \n11.56 = p.<\/p>\n

    Question 5.
    \nUse a proportion to find each value.
    \na. 2% of 180
    \n\"Envision<\/p>\n

    Answer:
    \nn = 3.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2% of 180.
    \n2\/100 = n\/180.
    \n0.02 = n\/180.
    \nn = 0.02 x 180.
    \nn = 3.6.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    b. What percent is 17 out of 40?
    \n\"Envision<\/p>\n

    Answer:
    \np = 6.8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n17\/100 = p\/40.
    \n0.17 = p\/40.
    \np = 0.17 x 40.
    \np = 6.8.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 6.
    \nConstruct Arguments<\/strong> Gia researches online that her car is worth $3,000. She hopes to sell it for 85% of that value, but she wants to get at least 70%. She ends up selling it for $1,800. Did she get what she wanted? Justify your answer.<\/p>\n

    Answer:
    \nYes, she gets what she wanted.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nGia researches online that her car is worth $3,000.
    \nshe hopes to sell it for 85% of that value, but she wants to get at least 70%.
    \nShe ends up selling it for $1,800.
    \n85\/100 x 3000.
    \n0.85 x 3000.
    \n70\/100 x 1800.
    \n0.7 x 1800.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7-8, fill in the boxes to solve.
    \nQuestion 7.
    \nThe rabbit population in a certain area is 200% of last year’s population. There are 1,100 rabbits this year. How many were there last year?
    \n\\(\\frac{1,100}{w}\\) = \\(\\frac{}{}\\)
    \nThere were _______ rabbits last year.<\/p>\n

    Answer:
    \nThe number of rabbits last year = 2200.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe rabbit population in a certain area is 200% of last year’s population.
    \nThere are 1,100 rabbits this year.
    \n1100\/w = 200\/100.
    \n1100\/w = 2.
    \nw = 2 x 1100.
    \nw = 2200.
    \nso the number of rabbits last year = 2200.<\/p>\n

    Question 8.
    \nA company that makes hair-care products had 3,000 people try a new shampoo. Of the 3,000 people, 9 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
    \n\\(\\frac{9}{3,200}\\) = \\(\\frac{p}{}\\)
    \nPercent = _________%<\/p>\n

    Answer:
    \nThe percent of the people who had a mild allergic reaction = 8.4%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA company that makes hair-care products had 3,000 people try a new shampoo.
    \nOf the 3,000 people, 9 had a mild allergic reaction.
    \n9\/3200 = p\/3000.
    \n0.0028 = p\/3000.
    \np = 3000 x 0.0028.
    \np = 8.4%.
    \nso the percent of the people had a mild allergic reaction = 8.4%.<\/p>\n

    Question 9.
    \nA survey was given to people who owned a certain type of car. What percent of the people surveyed were completely satisfied with the car?
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent of the people surveyed were completely satisfied with the car = 1100.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA survey was given to people who owned a certain type of car.
    \ncompletely satisfied = 1100.
    \nsomewhat satisfied = 740%.
    \nnot satisfied = 160%.
    \nso the percent of the people surveyed were completely satisfied with thw car = 1100%.<\/p>\n

    Question 10.
    \nThe Washingtons buy a studio apartment for $240,000. They pay a down payment of $60,000
    \na. Their down payment is what percent of the purchase price?<\/p>\n

    Answer:
    \nThe down payment is 0.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe Washingtons buy a studio apartment for $240,000.
    \nThey pay a down payment of $60,000.
    \n240000\/60000 = 0.4.<\/p>\n

    b. What percent of the purchase price would a $12,000 down payment be?<\/p>\n

    Answer:
    \nThe percent of the purchase price would be a $12000 down payment = $20.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe Washingtons buy a studio apartment for $240,000.
    \n240000\/12000 = 20.
    \nso the percent of the purchase price would be a $120000 down payment = $20.<\/p>\n

    Question 11.
    \nA restaurant customer left $3.50 as a tip. The tax on the meal was 7% and the tip was 20% of the cost including tax.
    \n\"Envision
    \na. What piece of information is not needed to compute the bill after tax and tip?<\/p>\n

    Answer:
    \nThe piece of information is not needed to compute the bill after tax and tip = $0.455.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA restaurant customer left $3.50 as a tip.
    \nThe tax on the meal was 7% and the tip was 20% of the cost including tax.
    \n20% – 7% = 13%.
    \n13\/100 = 0.13.
    \n3.50 x 0.13 = 0.455.
    \nso the piece of information is not needed to compute the bill after tax and tip = $0.455.<\/p>\n

    b. Make Sense and Persevere What was the total bill?<\/p>\n

    Answer:<\/p>\n

    Question 12.
    \nReasoning<\/strong> What is a good estimate for 380% of 60? Explain.<\/p>\n

    Answer:
    \nThe good estimate is 228.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n380% of 60.
    \n380\/100 x 60.
    \n3.8 x 60 = 228.
    \nso the good estimate is 228.<\/p>\n

    Question 13.
    \nCritique Reasoning<\/strong> Marna thinks that about 35% of her mail is junk mail. She gets about twice as much regular mail as junk mail. Is she correct? Explain.<\/p>\n

    Answer:
    \nYes, she was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMarna thinks that about 35% of her mail is junk mail.
    \nShe gets about twice as much regular mail as junk mail.
    \n35% + 35%.
    \n70%.
    \n70\/100 = 0.7.
    \nso she was correct.<\/p>\n

    Question 14.
    \nHypatia has read 13 chapters of a 22-chapter book. What percent of the chapters has she read?<\/p>\n

    Answer:
    \nThe chapters she has read = 9%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHypatia has read 13 chapters of a 22-chapter book.
    \n22 – 13 = 9.
    \n9 percent = 9\/100.
    \nso 9% of the chapters has she read.<\/p>\n

    Question 15.
    \nA school year has 4 quarters. What percent of a school year is 7 quarters?<\/p>\n

    Answer:
    \nThe percent of a school year = 28%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA school year has 4 quarters.
    \n4\/100 = 7\/q.
    \n0.04 = 7\/q.
    \nq = 0.04 x 7.
    \nq = 0.28.
    \nso the percent of a school year = 28%.<\/p>\n

    Question 16.
    \nConstruct Arguments<\/strong> A survey found that 27% of high school students and 94% of teachers and school employees drive to school. The ratio of students to employees is about 10 to 1. Roger states that the number of students who drive to school is greater than the number of teachers and employees who drive to school. Explain how Roger’s statement could be correct.<\/p>\n

    Answer:
    \nThe ratio of students to employees is about 10 to 1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA survey found that 27% of high school students and 94% of teachers and school employees.
    \nThe ratio of students to employees is about 10 to 1.
    \n27\/100 = 0.27.
    \n94\/100 = 0.94.
    \nso the ratio of students to employees is about 10 to 1.<\/p>\n

    Question 17.
    \nHigher Order Thinking<\/strong> Stefan sells Jin a bicycle for $114 and a helmet for $18. The total cost for Jin is 120% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
    \n\"Envision<\/p>\n

    Answer:
    \nThe money did he make by selling the bicycle and helmet to Jin = $132.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nStefan sells Jin a bicycle for $114 and a helmet for $18.
    \nThe total cost for Jin is 120% of what Stefan spent originally to buy the bike and helmet.
    \n$114 + $18 = $132.
    \nso the money did he make by selling the bicycle and helmet to Jin = $132.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 18.
    \nLast month Nicole spent $30. This month she spent 140% of what she spent last month. Write a proportional equation to represent the situation. How much did Nicole spend this month?<\/p>\n

    Answer:
    \nThe amount did Nicole spend this month = $42.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLast month Nicole spent $30.
    \nThis month she spent 140% of what she spent last month.
    \n140\/100 x $30.
    \n1.4 x $30.
    \n$42.
    \nso the amount did Nicole spend this month = $42.<\/p>\n

    Question 19.
    \nMr. Jones, the owner of a small store buys kayak paddles for $50.00 each, and sells them for 180% of the purchase price.
    \nPART A
    \nA customer buys a paddle for $97.65, which includes the selling price and sales tax. What is the sales tax rate?
    \nA 7.65%
    \nB. 4.7%
    \nC. 9.75%
    \nD. 8.5%<\/p>\n

    Answer:
    \nOption C was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMr. Jones, the owner of a small store buys kayak paddles for $50.00 each and sells them for 180% of the purchase price.
    \nA customer buys a paddle for $97.65, which includes the selling price and sales tax.
    \n180\/100 = 1.8.
    \n1.8 x 50.
    \n90.
    \nso option C was correct.<\/p>\n

    PART B
    \nIf Mr. Jones buys paddles for $35 instead of $50, and uses the same percent increase on price, how many paddles must Mr. Jones sell for the total paddle sales, before tax, to be at least $250? Explain your answer.<\/p>\n

    Answer:
    \nMr. Jones sells for the total paddle sales = $40.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIf Mr. Jones buys paddles for $35 instead of $50 and uses the same percent increase on the price.
    \n$250\/$50.
    \n$.5.
    \n$35 + $5 = $40.<\/p>\n

    Lesson 3.3 Represent and Use the Percent Equation<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nFran is shopping for a new pair of shoes. She did some research and has narrowed the options to the two pairs she likes the most. Based on buyers’ reviews, which pair do you recommend that she buy? Explain your thinking.<\/p>\n

    I can.. represent and solve percent problems using equations.
    \n\"Envision<\/p>\n

    Model with Math
    \nHow can you use what you know about ratios to compare the reviews?<\/p>\n

    Focus on math practices
    \nModel with Math Describe another situation in which you could use ratios to make a decision.<\/p>\n

    Essential Question<\/strong>
    \nHow are percent problems related to proportional reasoning?<\/p>\n

    Try It!<\/strong><\/p>\n

    An elephant weighs 15,000 pounds on Earth and 2,500 pounds on the Moon. Assuming the weights are proportional, what percent of its weight on Earth is its weight on the Moon?
    \n\"Envision
    \nThe elephant’s weight on the Moon is about __________% of its weight on Earth.<\/p>\n

    Answer:
    \nThe elephant’s weight on the Moon is about 6% of its weight on Earth.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn elephant weighs 15,000 pounds on Earth and 2,500 pounds on the Moon.
    \nAssuming the weights are proportional.
    \n2500 = p x 15000.
    \np = 15000\/2500.
    \np = 6.
    \nso the elephant’s weight on the Moon is about 6% of its weight on Earth.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Convince Me! How does the percent describe how the weights are related?<\/p>\n

    Try It!<\/strong><\/p>\n

    To make a profit, a clothing store sells board shorts at 115% of the amount they paid for them. How much did the store pay for the board shorts shown?
    \n\"Envision<\/p>\n

    Answer:
    \nThe store pays for the board shorts = $32.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTo make a profit, a clothing store sells board shorts at 115% of the amount they paid for them.
    \nthe cost of the short is $28.
    \n115\/100 x $28.
    \n1.15 x\u00a0 $28 = $32.2.
    \nso the store pay for the board shorts = $32.2.<\/p>\n

    KEY CONCEPT<\/strong><\/p>\n

    The percent equation shows how a percent relates proportional quantities. The percent is a constant of proportionality and the equation has the same form as y = mx.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question How are percent problems related to proportional reasoning?<\/p>\n

    Answer:
    \nThe percent problem related to proportional reasoning is y = mx.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe percent equation shows how a percent relates to proportional quantities.
    \nThe percent is a constant of proportionality and the equation has the same form as y = mx.
    \npart\/whole = percent.
    \npart = percent x whole.<\/p>\n

    Question 2.
    \nReasoning<\/strong> A waiter at a restaurant receives $11 as a tip on a $47.20 bill. He usually receives tips that are 20% of the total bill. Is the tip amount what the waiter typically receives? Explain.<\/p>\n

    Answer:
    \nThe tip amount is the waiter typically receives = $11.64.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA waiter at a restaurant receives $11 as a tip on a $47.20 bill.
    \nHe usually receives tips that are 20% of the total bill.
    \n$47.20 + $11.
    \n$58.2.
    \n20\/100 x $58.2.
    \n0.2 x $58.2 = $11.64.<\/p>\n

    Question 3.
    \nConstruct Arguments<\/strong> Sara used an equation to solve the problem below. Justify each step of her work. About 11% of people are left-handed. How many people would you expect to be left-handed in a class of 30 students?
    \nl = 0.11 \u2022 30
    \n\u013c = 3.3
    \nabout 3 students<\/p>\n

    Answer:
    \nThe number of people would you accept to be left-handed = 3 students.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n11% of people are left-handed.
    \n11\/100 x 30.
    \n0.11 x 30 = 3.3.
    \nso the number of people would you accept to be left-handed = 3 students.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nAn auto insurance company pays 12% commission to its agents for each new insurance policy they sell. How much commission does an agent make on a $1,000 policy?<\/p>\n

    Answer:
    \nThe commission does an agent makes on a $1000 policy = $10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn auto insurance company pays a 12% commission to its agents for each new insurance policy they sell.
    \n12\/100 x $1000.
    \n0.12 x $1000.
    \n$10.
    \nso the commission does an agent make on a $1000 policy = $10.<\/p>\n

    Question 5.
    \nCurt and Melanie are mixing blue and yellow paint to make seafoam green paint. Use the percent equation to find how much yellow paint they should use.
    \n\"Envision<\/p>\n

    Answer:
    \nThe quantity of yellow paint they should use = 1.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCurt and Melanie are mixing blue and yellow paint to make seafoam green paint.
    \n70% = 70\/100.
    \n70\/100 = 0.7.
    \n30\/100 = 30%.
    \n30% = 0.3.
    \n0.3 + 0.7 = 1.
    \n1 x 1.5 = 1.5.
    \nso the quantity of yellow paint they should use = 1.5.<\/p>\n

    Question 6.
    \nBill paid $35.99 in tax on a laptop that cost $449.99. About what percent sales tax did Bill pay?<\/p>\n

    Answer:
    \nThe percent sales tax did Bill pay = 4.8%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nBill paid $35.99 in tax on a laptop that cost $449.99
    \n$449.99 + $35.99.
    \n$485.98.
    \nso the percent of sales tax did Bill pay = 4.8%.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7 and 8, solve each percent problem.
    \nQuestion 7.
    \nIn a survey of 500 voters, 430 said they would vote for the same candidate again. What percent of the voters would vote the same way again?
    \npart = percent. whole
    \n_______ = p% \u2022 ________
    \n_______ = p%<\/p>\n

    Answer:
    \nThe percent of the votes would vote the same way again = 0.086.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIn a survey of 500 voters, 430 said they would vote for the same candidate again.
    \n500 = p% x 430.
    \np% = 430\/500.
    \np% = 0.86.
    \np = 0.086.
    \nso the percent of the votes would vote the same way again = 0.086.<\/p>\n

    Question 8.
    \nThe local newspaper has letters to the editor from 40 people. If this number represents 5% of all of the newspaper’s readers, how many readers, r, does the newspaper have?
    \npart = percent. whole
    \n______ = ______ \u2022 r
    \n______ = r<\/p>\n

    Answer:
    \nThe number of readers r does the newspaper have = 0.00125.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe local newspaper has letters to the editor from 40 people.
    \nIf this number represents 5% of all of the newspaper’s readers.
    \n5% = 40 x r.
    \n5\/100 = 40 x r.
    \n0.05 = 40r.
    \nr = 0.05\/40.
    \nr = 0.00125.
    \nso the number of readers r does the newspaper have = 0.00125.<\/p>\n

    Question 9.
    \nMake Sense and Persevere What percent of the 16-gigabyte hard drive shown is used for photos?
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent of the 16-gigabyte hard drive shown is used for photos = 0.002075.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \npercent = part\/whole.
    \npercent = 3.32\/16.
    \npercent = 0.2075.
    \n0.2075% = 0.002075.
    \nso the percent of the 16-gigabyte hard drive shown is used for photos = 0.002075.<\/p>\n

    Question 10.
    \nA shirt that normally costs $30 is on sale for $21.75. What percent of the regular price is the sale price?<\/p>\n

    Answer:
    \nThe percent of the regular price = 0.0825.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA shirt that normally costs $30 is on sale for $21.75.
    \n$30 – $21.75 = $8.25.
    \n$8.25% = 0.0825.
    \nso the percent of the regular price = 0.0825.<\/p>\n

    Question 11.
    \nComplete the table.
    \n\"Envision<\/p>\n

    Answer:
    \nThe commission = $30.72.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe sales of the earning commission = $768.
    \nthe commission rate = 4%.
    \n4\/100 = 768\/c.
    \n0.04 = 768\/c.
    \nc = 0.04 x 768.
    \nc = $30.72.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 12.
    \nComplete the table.
    \n\"Envision<\/p>\n

    Answer:
    \nThe sales tax = $1.7991.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe selling price is $39.98.
    \nthe tax rate is 4.5%.
    \n4.5 \/100 x $39.98.
    \n0.045 x $39.98.
    \n$1.7991.
    \nso the sales tax = $1.7991.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 13.
    \nA restaurant automatically charges a 20% gratuity if a party has 6 or more people. How much gratuity is added to a party of 6 on a $141 bill?<\/p>\n

    Answer:
    \nThe much gratuity is added to a party of 6 on a $141 bill = $169.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA restaurant automatically charges a 20% gratuity if a party has 6 or more people.
    \n20\/100 = 0.2.
    \n0.2 x 6 = 1.2.
    \n1.2 x $141 = 169.2.<\/p>\n

    Question 14.
    \nMake Sense and Persevere A large university accepts 70% of the students who apply. Of the students the university accepts, 25% actually enroll. If 20,000 students apply, how many enroll?<\/p>\n

    Answer:
    \nThe number of students that enroll = 200 students.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA large university accepts 70% of the students who apply.
    \nOf the students the university accepts, 25% actually enroll.
    \n70 + 25 = 95.
    \n95\/100 x 20000.
    \n0.95 x 20000.
    \n200.
    \nso the number of students that enroll = 200 students.<\/p>\n

    Question 15.
    \nModel with Math There are 4,000 books in the town’s library. Of these, 2,600 are fiction. Write a percent equation that you can use to find the percent of the books that are fiction. Then solve your equation.<\/p>\n

    Answer:
    \nThe percent of the books that are fiction = 0.01538.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 4,000 books in the town’s library.
    \nOf these, 2,600 are fiction.
    \n4000\/2600 = 1.538.
    \n1.538% = 0.01538.<\/p>\n

    Question 16.
    \nA salesperson earns 4% commission on furnace sales.
    \na. What is the commission that the salesperson earns on the sale of $33,000 worth of furnaces?<\/p>\n

    Answer:
    \nThe salesperson earns on the sale of $33000 = $1320.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA salesperson earns a 4% commission on furnace sales.
    \n4\/100 x $33000.
    \n0.04 x $33000.
    \n$1320.
    \nso the salesperson earns on the sale of $33000 = $1320.<\/p>\n

    b. Suppose the salesperson doubles his sales of furnaces. What would be true about the commission? Explain without using any calculations.<\/p>\n

    Answer:
    \nThe salesperson doubles his sales of furnaces = $2640.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA salesperson earns a 4% commission on furnace sales.
    \n4\/100 x $33000.
    \n0.04 x $33000.
    \n$1320.
    \n1320 x $2 = $2640.
    \nso the salesperson doubles his sales of furnaces = $2640.<\/p>\n

    Question 17.
    \nHeidi earns 3% commission on the jewelry she sells each week. Last week, she sold the pieces of jewelry shown.
    \n\"Envision
    \na. How much did she make in commission?
    \nAnswer:
    \nShe makes in commission is 21.9%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHeidi earns 3% commission on the jewelry she sells each week.
    \n$110 + $275 + $200 + $145.
    \n$730.
    \n3% of $730.
    \n3\/100 x 730.
    \n0.03 x 730.
    \n21.9.<\/p>\n

    b. Reasoning How much did the jewelry store take in from her sales? How do you know?<\/p>\n

    Answer:
    \nThe jewelry store takes in from her sales 29.2%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHeidi earns 3% commission on the jewelry she sells each week.
    \n$110 + $275 + $200 + $145.
    \n$730.
    \n4% of $730.
    \n4\/100 x 730.
    \n0.04 x 730.
    \n29.2.<\/p>\n

    Question 18.
    \nHigher Order Thinking<\/strong> in a company, 60% of the workers are men. If 1,380 women work for the company, how many workers are there in all? Show two different ways that you can solve this problem.<\/p>\n

    Answer:
    \nThe number of workers in all = 828 workers.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIn a company, 60% of the workers are men.
    \nIf 1,380 women work for the company.
    \n60% of 1380.
    \n60\/100 x 1380.
    \n6\/10 x 1380.
    \n0.6 x 1380.
    \n828.
    \nso the number of workers in all = 828 workers.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 19.
    \nA salesperson starts working 40 hours per week at a job with two options for being paid. Option A is an hourly wage of $19. Option B is a commission rate of 8% on weekly sales. How much does the salesperson need to sell in a given week to earn the same amount with each option?
    \nA. $9,500
    \nB. $4,750
    \nC. $760
    \nD. $320<\/p>\n

    Answer:
    \nThe salesperson needs to sell in a given week to earn the same amount with each option = $320.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA salesperson starts working 40 hours per week at a job with two options for being paid.
    \nOption A is an hourly wage of $19. Option B is a commission rate of 8% on weekly sales.
    \n8\/100 x 40.
    \n0.08 x 40.
    \n3.2.
    \nso the salesperson needs to sell in a given week to earn the same amount with each option = $320.<\/p>\n

    Question 20.
    \nAt a real estate agency, an agent sold a house for $382,000. The commission rate is 5.5% for the real estate agency. The commission for the agent is 30% of the amount the real estate agency gets. How much did the agent earn in commission? Explain your answer.<\/p>\n

    Answer:
    \nThe agent earn in commission = $114600.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAt a real estate agency, an agent sold a house for $382,000.
    \nThe commission rate is 5.5% for the real estate agency.
    \nThe commission for the agent is 30% of the amount the real estate agency gets.
    \n30\/100 x $382000.
    \n0.3 x $382000.
    \n114600.
    \nso the agent earn in commission = $114600.<\/p>\n

    Topic 3 Mid-Topic Checkpoint<\/h3>\n

    Question 1.
    \nVocabulary<\/strong> Explain how the percent equation relates proportional quantities. Lesson 3-3<\/p>\n

    Answer:
    \nThe percent equation shows how a percent relates to proportional quantities.
    \ny = mx.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe percent equation shows how a percent relates proportional quantities.
    \nThe percent is a constant of proportionality and the equation has the same form as y = mx.
    \npart\/whole = percent.
    \npart = percent x whole.<\/p>\n

    Question 2.
    \nColleen buys a movie for $20 and pays 7% sales tax. Her cousin, Brad, lives in another state. Brad buys the same movie for $22 and pays 6% sales tax. Who pays more sales tax? How much more? Lessons 3-1 and 3-3<\/p>\n

    Answer:
    \nBrad pays more sales tax = $0.1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nColleen buys a movie for $20 and pays 7% sales tax.
    \nHer cousin, Brad, lives in another state.
    \nBrad buys the same movie for $22 and pays 6% sales tax.
    \n7\/100 x $20.
    \n0.07 x 20 = $1.4.
    \n6\/100 x $22.
    \n0.06 x 22 = $1.3.
    \nBrad pays more sales tax = $0.1.<\/p>\n

    Question 3.
    \nKamesh and Paolo each read 40 books in one year. Kamesh read 12 nonfiction books. Thirty-five percent of the books Paolo read were nonfiction. Who read more nonfiction books? How many more? Lesson 3-2<\/p>\n

    Answer:
    \nKamesh read more notifications.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKamesh and Paolo each read 40 books in one year.
    \nKamesh read 12 nonfiction books.
    \nThirty-five percent of the books Paolo read were nonfiction.
    \n35% x 40.
    \n0.35 x 40 = $14.
    \n35% x 12.
    \n0.35 x 12 = $4.2.
    \nso Kamesh read more notifications.<\/p>\n

    Question 4.
    \nVal buys a computer for $920. If this is 115% of what the store paid for the same computer, how much did the store earn on the sale? Lesson 3-3<\/p>\n

    Answer:
    \nThe much did the store earn on the sale = $1058.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nVal buys a computer for $920.
    \nIf this is 115% of what the store paid for the same computer.
    \n115\/100 x $920.
    \n1.15 x $920 = $1058.
    \nso the much did the store earn on the sale = $1058.<\/p>\n

    Question 5.
    \nFor each situation, select the percent to answer the question. Lessons 3-1, 3-2, and 3-3<\/p>\n

    Answer:
    \n25%, 5%, and 5%<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIn an auto repair shop, 14 of the 56 cars received oil changes.
    \n14\/56 = 0.25.
    \n0.25 x 100 = 25%.
    \nHarry pays $3.50 sales tax on a $70 item.
    \nIn a box of 250 paperclips, 50 are red.
    \n250\/50 = 5%.<\/p>\n

    \"Envision<\/p>\n

    Question 6.
    \nExplain how you can use proportional reasoning to determine the whole if you know that 21 is 60% of the whole. Lesson 3-2<\/p>\n

    Answer:
    \n12.6%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n21 is 60%.
    \n60\/100 x 21.
    \n0.6 x 21.
    \n12.6.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Topic 3 Mid-Topic Performance Task<\/h3>\n

    The coach of a women’s basketball team wants each of her starting players to make at least 75% of the free throws attempted during regular season games. The table shows the statistics for the starting players after the first 15 games.
    \n\"Envision<\/p>\n

    PART A
    \nUse the table. Find the percentage of free throws made by each player. Round to the nearest whole percent.<\/p>\n

    Answer:
    \nThe percentage of free throws made by each player = 1.5%, 1.1%, 1.4%, 1.8%, and 0.7%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nWilson free throws attempted = 36\/24 = 1.5.
    \nBartholdi free throws attempted = 42\/37 = 1.1.
    \nJhonson free throws attempted = 22\/15 = 1.4.
    \nGarcia free throws attempted = 29\/16 = 1.8.
    \nO’Malley free throws attempted = 14\/12 = 0.7.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    PART B
    \nChoose one of the players with a free-throw percentage less than 75%. Determine a number of free throws the player could attempt and make during the next 10 games to increase her free-throw percentage to at least 75%.
    \nAnswer:<\/p>\n

    PART C
    \nChoose one of the players with a free-throw percentage greater than 75%. Determine the number of free throws that the player could miss during the next 10 games and still maintain an overall percentage of at least 75%.
    \nAnswer:<\/p>\n

    Lesson 3.4 Solve Percent Change and Percent Error Problems<\/h3>\n

    Explain It!<\/strong>
    \nNadia lives in the town of Bayville. Quinn lives in the town of Portside. Nadia and Quinn each claim that her respective town’s population is growing more rapidly.<\/p>\n

    I can… solve problems involving percent change and percent error.
    \n\"Envision<\/p>\n

    A. Write an argument to support Nadia. Why might she argue that Bayville’s population is growing more rapidly?<\/p>\n

    Answer:
    \nThe population is growing more rapidly because they have the Historic place, LightHouse, and Beachfront.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNadia lives in the town of Bayville.
    \nQuinn lives in the town of Portside.
    \nNadia’s population has last year 3399.
    \nQuinn has population has 1870.
    \nNadia population has this year 3702.
    \nQuinn’s population has 1926.
    \nNadia has a Historic place, LightHouse, and Beachfront.
    \nso the population is growing more rapidly.<\/p>\n

    B. Write an argument to support Quinn. Why might she argue that Portside’s population is growing more rapidly?<\/p>\n

    Answer:
    \nThe population is growing more rapidly because they have the Aquarium.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNadia lives in the town of Bayville.
    \nQuinn lives in the town of Portside.
    \nNadia’s population has last year 3399.
    \nQuinn has population has 1870.
    \nNadia population has this year 3702.
    \nQuinn’s population has 1926.
    \nQuinn has a Historic place, LightHouse, and Beachfront.
    \nso the population is growing more rapidly.<\/p>\n

    c. Whose reasoning is more logical? Explain why.<\/p>\n

    Answer:
    \nNadia’s reasoning is more logical.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNadia lives in the town of Bayville.
    \nQuinn lives in the town of Portside.
    \nNadia’s population has last year 3399.
    \nQuinn has population has 1870.
    \nNadia population has this year 3702.
    \nQuinn’s population has 1926.
    \nthe population of Nadia is very high.
    \nso Nadia’s reasoning is more logical.<\/p>\n

    Focus on math practices
    \nCritique Reasoning Suppose Bayville’s population is expected to grow 3% next year. Nadia says that means the population will increase by 300 people. Is Nadia’s reasoning correct? Explain.<\/p>\n

    Answer:
    \nYes, Nadia was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nBayville’s population is expected to grow 3% next year.
    \n3\/100 = 0.03.
    \n300.
    \nso Nadia was correct.<\/p>\n

    Essential Question<\/strong>
    \nHow is finding percent error similar to finding percent change?<\/p>\n

    Try It!<\/strong><\/p>\n

    What will be the length of the alligator next year if its length changes by the same percent as it changed this year?
    \npercent change \u2022 length this year = change in length
    \n\"Envision
    \n0.1875 \u2022 ________ = ________
    \n_______ + _______ = ________
    \nNext year, the length of the alligator will be ________ inches long.<\/p>\n

    Answer:
    \nNext year, the length of the alligator will be 45 inches long.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \npercent change \u2022 length this year = change in length.
    \n0.1875 x 38 = 7.125.
    \n7.125 + 38 = 45.125.
    \nso next year, the length of the alligator will be 45 inches long.<\/p>\n

    Convince Me! Why is the increase in the alligator’s length different from year to year, even though the percent change stayed the same?<\/p>\n

    Try It!<\/strong><\/p>\n

    The specification for the length of a bolt is 4.75 inches. A machinist makes a bolt that is 4.769 inches long. What is the percent error of the bolt’s length?
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent error of the bolt’s = 0.019.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe specification for the length of a bolt is 4.75 inches.
    \nA machinist makes a bolt that is 4.769 inches long.
    \n4.769 – 4.75 = 0.019.
    \nso the percent error of the bolt’s = 0.019.<\/p>\n

    KEY CONCEPT<\/strong><\/p>\n

    Percent change and percent error problems are kinds of percent problems. You can use the percent equation to solve them.
    \namount of change = percent change \u2022 original amount
    \nThe amount of change is the difference between original and new values
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How is finding percent error similar to finding percent change?<\/p>\n

    Answer:
    \nYes, percent error and percent change problems are the same.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPercent change and percent error problems are kinds of percent problems.
    \namount of change = percent change \u2022 original amount.
    \nThe amount of change is the difference between original and new values.<\/p>\n

    Question 2.
    \nReasoning<\/strong> Give an example of a problem in which the percent error is greater than 20%, but less than 50%. Explain how you determined the percent error.<\/p>\n

    Answer:
    \nThe percent error is less than 20% but less than 50%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \npercent error = percent change x original amount.
    \npercent error = 5% x 3%.
    \npercent error = 15%.
    \nso the percent error is less than 20% but less than 50%.<\/p>\n

    Question 3.
    \nConstruct Arguments<\/strong> A store manager marked up a $10 flash drive by 20%. She then marked it down by 20%. Explain why the new price of the flash drive is not $10.<\/p>\n

    Answer:
    \nThe new price of the flash drives is $2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA store manager marked up a $10 flash drive by 20%.
    \nShe then marked it down by 20%.
    \n20\/100 x 10.
    \n0.2 x 10 = 2.
    \nso the new price of the flash drives is $2.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nLita’s softball team won 8 games last month and 10 this month. What was the percent change in games the team won? Was it an increase or decrease?<\/p>\n

    Answer:
    \nThe percent change in games the team won = 80.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLita’s softball team won 8 games last month and 10 this month.
    \npercent change = percent change x original amount.
    \npercent change = 8 x 10.
    \npercent change = 80.<\/p>\n

    Question 5.
    \nWhat is the percent change in the price of a gallon of gas, to the nearest whole percent? Is it an increase or a decrease?
    \n\"Envision<\/p>\n

    Answer:
    \nThe percent change in the price of a gallon of gas = 42.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3.499 last year.
    \n3.079 this year.
    \n3.499 – 3.079 = 0.42.
    \n42\/100 = 42.
    \nso the percent change in the price of a gallon of gas = 42.<\/p>\n

    Question 6.
    \nSeveral students measured a 25-mm-long nail and wrote the measurements shown in the table below. Whose measurement had the greatest percent error? Round to the nearest percent.
    \n\"Envision<\/p>\n

    Answer:
    \nTenicia has the greatest percent error.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSeveral students measured a 25-mm-long nail and wrote the measurements.
    \n26 – 25 = 1.
    \n25 – 23 = 2.
    \n25 – 25 = 0.
    \nso Tenicia had the greatest measurement.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7-8, use the bar diagram and fill in the boxes to solve.
    \nQuestion 7.
    \nThe original quantity is 10 and the new quantity is 13. What is the percent change? Is it an increase or decrease?
    \n\"Envision
    \nThe percent decrease is _______ %.<\/p>\n

    Answer:
    \nThe percent decrease is 1.3%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe original quantity is 10 and the new quantity is 13.
    \npercent change = 10 x 13.
    \npercent change = 130.
    \n130\/100 = 1.3.
    \nso the percent decrease is 1.3%.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 8.
    \nThe original quantity is 5 and the new quantity is 3. What is the percent change? Is it an increase or decrease?
    \n\"Envision
    \nThe percent increase is _______%.<\/p>\n

    Answer:
    \nThe percent increase is 0.006%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe original quantity is 10 and the new quantity is 13.
    \n3 = p x 5.
    \npercent change = 3\/5.
    \n0.6\/100 = 0.006..
    \nso the percent increase is 0.006%.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 9.
    \nAt noon, a tank contained 10 cm of water. After several hours, it contained 7 cm of water. What is the percent decrease of water in the tank?<\/p>\n

    Answer:
    \nThe percent decrease of water in the tank = 3%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAt noon, a tank contained 10 cm of water. After several hours, it contained 7 cm of water.
    \npercent change = 10 – 7.
    \npercent change = 3.
    \nso the percent decrease of water in the tank = 3%.<\/p>\n

    Question 10.
    \nCraig likes to collect vinyl records. Last year he had 10 records in his collection. Now he has 12 records. What is the percent increase of his collection?<\/p>\n

    Answer:
    \nThe percent increase of his collection = 2%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCraig likes to collect vinyl records. Last year he had 10 records in his collection.
    \nNow he has 12 records.
    \npercent increase = 12 – 10.
    \npercent increase = 2.
    \nso the percent increase of his collection = 2%.<\/p>\n

    Question 11.
    \nCarl bought an airline ticket. Two weeks ago, the cost of this flight was $300.
    \n\"Envision
    \nWhat is the percent increase?<\/p>\n

    Answer:
    \nThe percent increase = 75%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCarl bought an airline ticket. Two weeks ago, the cost of this flight was $300.
    \npercent increase = 375 – 300.
    \npercent increase = 75.
    \nso the percent increase = 75%.<\/p>\n

    Question 12.
    \nOn Monday, a museum had 150 visitors. On Tuesday, it had 260 visitors.
    \na. Estimate the percent change in the number of visitors to the museum.<\/p>\n

    Answer:
    \nThe percent change in the number of visitors to the museum = 39000.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOn Monday, a museum had 150 visitors. On Tuesday, it had 260 visitors.
    \npercent change = 150 x 260.
    \npercent change = 39000.
    \nso the percent change in the number of visitors to the museum = 39000.<\/p>\n

    b. About how many people would have to visit the museum on Wednesday to have the same percent change from Tuesday to Wednesday as from Monday to Tuesday? Explain your answer.<\/p>\n

    Answer:
    \nThe percent change from Tuesday to Wednesday = 110.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOn Monday, a museum had 150 visitors. On Tuesday, it had 260 visitors.
    \npercent change = 150 – 260.
    \npercent change = 110.
    \nso the percent change from Tuesday to Wednesday = 110.<\/p>\n

    Question 13.
    \nRihanna has a container with a volume of 1.5 liters. She estimates the volume to be 2.1 liters. What is the percent error?<\/p>\n

    Answer:
    \nThe percent error = 0.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nRihanna has a container with a volume of 1.5 liters.
    \nShe estimates the volume to be 2.1 liters.
    \npercent error is similar to the percent change.
    \npercent change = 2.1 – 1.5.
    \npercent change = 0.6.
    \nso the percent error = 0.6.<\/p>\n

    Question 14.
    \nThe label on a package of bolts says each bolt has a diameter of 0.35 inch. To be in the package, the percent error of the diameter must be less than 5%. One bolt has a diameter of 0.33 inch. Should it go in the package? Why or why not?<\/p>\n

    Answer:
    \nYes, it would go in the package.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe label on a package of bolts says each bolt has a diameter of 0.35 inches.
    \nTo be in the package, the percent error of the diameter must be less than 5%. One bolt has a diameter of 0.33 inches.
    \npercent error = 0.35 – 0.33.
    \npercent error = 0.02.
    \n5\/100 x 0.02 = 0.05 x 0.02.
    \n0.001.
    \nit would go in the package.<\/p>\n

    Question 15.
    \nA band expects to have 16 songs on their next album. The band writes and records 62.5% more songs than they expect to have in the album. During the editing process, 50% of the songs are removed. How many songs will there be in the final album?<\/p>\n

    Answer:
    \nThe number of songs will there be in the final album = 200.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA band expects to have 16 songs on their next album.
    \nThe band writes and records 62.5% more songs than they expect to have in the album.
    \nDuring the editing process, 50% of the songs are removed.
    \n50% – 62.5% = 12.5%.
    \n12.5% x 16.
    \n200.
    \nso the number of songs will there be in the final album = 200.<\/p>\n

    Question 16.
    \nMake Sense and Persevere in the first week of July, a record 1,060 people went to the local swimming pool. In the second week, 105 fewer people went to the pool. In the third week, 135 more people went to the pool than in the second week. In the fourth week, 136 fewer people went to the pool than in the third week.
    \nWhat is the percent change in the number of people who went to the pool between the first and last weeks?<\/p>\n

    Answer:
    \nThe percent change in the number of people who went to the pool between the first and last weeks = 924.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPersevere in the first week of July, a record 1,060 people went to the local swimming pool.
    \nIn the second week, 105 fewer people went to the pool. In the third week, 135 more people went to the pool than in the second week.
    \nIn the fourth week, 136 fewer people went to the pool than in the third week.
    \npercent change =1060 – 136.
    \npercent change = 924.
    \nso the percent change in the number of people between first and last weeks = 924.<\/p>\n

    Question 17.
    \nBe Precise<\/strong> You have 20 quarters. You find 40% more quarters in your room. Then you go shopping and spend 50% of the total number of quarters.
    \na. Write an expression that represents the total number of quarters you take with you when you go shopping.<\/p>\n

    Answer:
    \nThe total number of quarters you take with you when you go shopping = 2 quarters.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nYou have 20 quarters. You find 40% more quarters in your room.
    \nThen you go shopping and spend 50% of the total number of quarters.
    \n50 – 40 = 10%.
    \n20 x 10\/100.
    \n20 x 0.1.
    \n2.
    \nso the total number of quarters you take with you and go shopping = 2 quarters.<\/p>\n

    b. How much money do you have left?<\/p>\n

    Answer:
    \nThe money I have left = 18 quarters.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nYou have 20 quarters. You find 40% more quarters in your room.
    \nThen you go shopping and spend 50% of the total number of quarters.
    \n20 – 2 = 18.
    \nso the money I have left = 18 quarters.<\/p>\n

    Question 18.
    \nHigher Order Thinking<\/strong> The dot plot shows predictions for the winning time in a 200-meter sprint. The winner finished the race in 22.3 seconds. Find the greatest percent error for a prediction to the nearest tenth of a percent. Justify your answer.
    \n\"Envision<\/p>\n

    Answer:
    \nThe greatest percent error for a prediction to the nearest tenth of a percent = 22.2 seconds.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe dot plot shows predictions for the winning time in a 200-meter sprint.
    \nThe winner finished the race in 22.3 seconds.
    \n200\/100 = 0.02%.
    \n22.3 – 0.02 = 22.2 seconds.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 19.
    \nThe amount of money in a savings account increases from $250 to $270 in one month. If the percent increase is the same for every month, how much money will be in the account at the end of the next month?
    \nA. $291.60
    \nB. $295
    \nC. $289.60
    \nD. $300<\/p>\n

    Answer:
    \nThe much money will be in the account at the end of the next month = 0.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe amount of money in the savings account increases from $250 to $270 in one month.
    \n270 – 250 = 20.
    \n20% = 20\/100.
    \n20\/100 = 0.2.<\/p>\n

    Question 20.
    \nA meteorologist predicted that there would be 1.0 inches of rainfall from a storm. Instead, there were 2.2 inches of rainfall. Which statements are true?
    \n\u2610 The prediction was off by 35%.
    \n\u2610 If the percent error should be less than 60%, the prediction was acceptable.
    \n\u2610 The percent error of the prediction was about 55%.
    \n\u2610 If the percent error should be less than 20%, the prediction was acceptable.
    \n\u2610 The difference between the predicted and actual rainfall was 1.2 inches.<\/p>\n

    Answer:
    \nThe statements are true is the difference between the predicted and actual rainfall was 1.2 inches.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA meteorologist predicted that there would be 1.0 inches of rainfall from a storm.
    \nInstead, there were 2.2 inches of rainfall.
    \n2.2 – 1.0 = 1.2.
    \nso the difference between predicted and actual rainfall = 1.2 inches.<\/p>\n

    3-ACT MATH<\/strong><\/p>\n

    3-Act Mathematical Modeling:
    \nThe Smart Shopper
    \n\"Envision<\/p>\n

    \u0410\u0421\u0422 1<\/p>\n

    Question 1.
    \nAfter watching the video, what is the first question that comes to mind?
    \nAnswer:<\/p>\n

    Question 2.
    \nWrite the Main Question you will answer.
    \nAnswer:<\/p>\n

    Question 3.
    \nConstruct Arguments<\/strong> Make a prediction to answer this Main Question. Explain how you arrived at your prediction.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 4.
    \nOn the number line below, write a number that is too small to be the answer. Write a number that is too large.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 5.
    \nPlot your prediction on the same number line.
    \nAnswer:<\/p>\n

    ACT 2<\/strong><\/p>\n

    Question 6.
    \nWhat information in this situation would be helpful to know? How would you use that information?
    \nAnswer:<\/p>\n

    Question 7.
    \nUse Appropriate Tools What tools can you use to solve the problem? Explain how you would use them strategically.
    \nAnswer:<\/p>\n

    Question 8.
    \nModel with Math Represent the situation using mathematics. Use your representation to answer the Main Question.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 9.
    \nWhat is your answer to the Main Question? Is it higher or lower than your prediction? Explain why.
    \n\"Envision
    \nAnswer:<\/p>\n

    ACT 3<\/strong><\/p>\n

    Question 10.
    \nWrite the answer you saw in the video.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 11.
    \nReasoning<\/strong> Does your answer match the answer in the video? If not, what are some reasons that would explain the difference?
    \nAnswer:<\/p>\n

    Question 12.
    \nMake Sense and Persevere Would you change your model now that you know the answer? Explain.
    \n\"Envision
    \nAnswer:<\/p>\n

    ACT 3<\/strong><\/p>\n

    Question 13.
    \nModel with Math Explain how you used a mathematical model to represent the situation. How did the model help you answer the Main Question?
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 14.
    \nBe Precise Describe how you would tell the friends to use their coupons.
    \nAnswer:<\/p>\n

    SEQUEL<\/strong>
    \nQuestion 15.
    \nMake Sense and Persevere Suppose the $20 coupon requires a purchase of $100 or more. How would that affect your solution?<\/p>\n

    Answer:
    \nThey affect the solution = $80.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSuppose the $20 coupon requires a purchase of $100 or more.
    \n$100 – $20 = $80.
    \nso they affect the solution = $80.<\/p>\n

    Lesson 3.5 Solve Markup and Markdown Problems<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nClare subscribes to an online music streaming service for a yearly fee of $96. Starting next month, there will be a 12% increase in the fee.
    \nThe ad for another music streaming service is shown below. Should Clare switch? Explain.<\/p>\n

    I can… solve problems involving percent markup and markdown.
    \n\"Envision<\/p>\n

    Model with Math
    \nYou can use the percent equation to determine the percent increase.<\/p>\n

    Focus on math practices
    \nMake Sense and Persevere What is another problem-solving method you could use to check that your solution makes sense?<\/p>\n

    Essential Question<\/strong>
    \nHow are the concepts of percent markup and percent markdown related to the percent equation?<\/p>\n

    Try It!<\/strong><\/p>\n

    What is the percent markup on a $300 phone sold for $465?
    \n\"Envision
    \nmarkup = percent markup \u2022 cost
    \n________ = p \u2022 300
    \n________ = p
    \nThe percent markup on the phone is _________%.<\/p>\n

    Answer:
    \nThe percent markup on the phone is 1.55%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe percent markup on a $300 phone sold for $465.
    \nmarkup = percent markup x cost.
    \nmarkup = p x 300.
    \n465\/300 = p.
    \np = 1.55.
    \nso the percent markup on the phone is 1.55%.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Convince Me! How does the percent equation help solve markup problems?<\/p>\n

    Try It!<\/strong><\/p>\n

    What is the selling price for a $45 pair of shoes with a 15% markup?<\/p>\n

    Answer:
    \nThe markup = 0.003.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe selling price = $45.
    \nmarkup = 15%.
    \nmarkup = percent markup x cost.
    \n15% = p x $45.
    \n0.15 = p x $45.
    \np = 0.15\/45.
    \np = 0.003.<\/p>\n

    Try It!<\/strong><\/p>\n

    Find the percent markdown for an $80 jacket that is on sale for $48.<\/p>\n

    Answer:
    \nThe markup = $32.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe selling price = $45.
    \nmarkup = 15%.
    \nmarkdown = $80 – $48.
    \nmarkdown = $32.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can solve markup and markdown problems using the percent equation.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How are the concepts of markup and markdown related to the percent equation?<\/p>\n

    Answer:
    \nmarkup and markdown are proportional to each other.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nmarkup = percent markup x original value.
    \nmarkdown = percent markdown x original value.
    \nmarkup = new value is greater than the original value.
    \nmarkdown = new value is less than the original value.<\/p>\n

    Question 2.
    \nReasoning<\/strong> What does the amount of the markup or markdown represent in the percent equation?<\/p>\n

    Answer:
    \nThe amount of the markup or markdown is proportional to each other.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nmarkup = percent markup x original value.
    \nmarkdown = percent markdown x original value.
    \nso the amount of the markup or markdown is proportional to each other.<\/p>\n

    Question 3.
    \nGeneralize When an item is marked up by a certain percent and then marked down by the same percent, is the sale price equal to the price before the markup and markdown?<\/p>\n

    Answer:
    \nmarkup = percent markup x original value.
    \nmarkdown = percent markdown x original value.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nWhen an item is marked up by a certain percent and then marked down by the same percent.
    \nmarkup = percent markup x original value.
    \nmarkdown = percent markdown x original value.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nAn item costs $4 before tax and $4.32 after sales tax. What is the sales tax rate?
    \n\"Envision<\/p>\n

    Answer:
    \nThe sales tax rate = $8.32.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn item costs $4 before tax and $4.32 after sales tax.
    \n$4 + $4.32.
    \n$8.32.
    \nso the sales tax rate = $8.32.<\/p>\n

    Question 5.
    \nSheila buys two concert tickets from her friend. She pays $90 for the two tickets. She looks at the tickets and sees that each ticket has a face value of $52.50.
    \na. How much of a markdown did her friend give Sheila? Explain how you know.<\/p>\n

    Answer:
    \nThe percent markdown = $1.174.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSheila buys two concert tickets from her friend. She pays $90 for the two tickets.
    \nShe looks at the tickets and sees that each ticket has a face value of $52.50.
    \nmarkdown = percent markdown x original value.
    \n$52.50 = percent markdown x $90.
    \npercent markdown = $90\/$52.50.
    \npercent markdown = $1.714.<\/p>\n

    b. What was the percent markdown, rounded to the nearest whole percent?<\/p>\n

    Answer:
    \nThe percent markdown rounded to the nearest whole percent = $2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSheila buys two concert tickets from her friend. She pays $90 for the two tickets.
    \nShe looks at the tickets and sees that each ticket has a face value of $52.50.
    \nmarkdown = percent markdown x original value.
    \n$52.50 = percent markdown x $90.
    \npercent markdown = $90\/$52.50.
    \npercent markdown = $1.714.
    \n$2.<\/p>\n

    Question 6.
    \nFind the sale prices.
    \na. $4,200 with a 35% markdown<\/p>\n

    Answer:
    \nThe sale price = $1470.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe sales price = percent markdown x original value.
    \nsales price = 35% x $4200.
    \nsales price = 0.35 x $4200.
    \nsales price = $1470.<\/p>\n

    b. $5,000 with a 44% markdown<\/p>\n

    Answer:
    \nThe sale price = $2200.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe sales price = percent markdown x original value.
    \nsales price = 44% x $5000.
    \nsales price = 0.44 x $5000.
    \nsales price = $2200.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7-8, fill in the boxes to solve.
    \nQuestion 7.
    \nA $300 suit is marked down by 20%. Find the sale price rounded to the nearest dollar.
    \nmarkdown = percent markdown \u2022 original price
    \nmarkdown = $_________
    \noriginal price – markdown = sale price
    \n$ _______ – $ ______
    \nsale price = $ ________<\/p>\n

    Answer:
    \nThe sale price = $300.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA $300 suit is marked down by 20%.
    \nsale price = original price – markdown.
    \nsale price = $300 – 20%.
    \nsale price = $300 – 0.2.
    \nsale price = $299.8.<\/p>\n

    Question 8.
    \nThe selling price of an item is $650 marked up from the wholesale cost of $450. Find the percent markup from wholesale cost to selling price.
    \nselling price – markup = wholesale cost
    \n$ _______ – $ ______ = $ _______
    \nmarkup = percent markup \u00d7 wholesale cost
    \n_______ = _______ \u00d7 _______
    \nThe percent markup is about ________.<\/p>\n

    Answer:
    \nThe markup = $250.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe selling price of an item is $650 marked up from the wholesale cost of $450.
    \nwholesale cost = selling price – markup.
    \n$450 = $650 – markup.
    \nmarkup = $250.<\/p>\n

    Question 9.
    \nKaren purchased the DVD player shown in the sign on the right. Find the percent markdown rounded to the nearest percent.
    \n\"Envision<\/p>\n

    Answer:
    \nThe markdown = 27,048.143.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKaren purchased the DVD player shown in the sign on the right.
    \nmarkdown = percent markdown x original value.
    \nmarkdown = $175.90 x $153.77.
    \nmarkdown = 27,048.143.<\/p>\n

    Question 10.
    \nA store manager instructs his employees to mark up all items by 30%. A store clerk puts a price tag of $30 on an item that the store bought for $27. As an employee, you notice that this selling price is incorrect.
    \na. Find the correct selling price. Round to the nearest dollar.<\/p>\n

    Answer:
    \nThe correct selling price is $3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA store manager instructs his employees to mark up all items by 30%.
    \nA store clerk puts a price tag of $30 on an item that the store-bought for $27.
    \nselling price = original price – mark up.
    \nselling price = $30 – $27.
    \nselling price = $3.
    \nso the correct selling price = $3.<\/p>\n

    b. What was the clerk’s likely error?<\/p>\n

    Answer:
    \nThe clerk’s likely error is he said his employees to mark up all items by 30%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA store clerk puts a price tag of $30 on an item that the store-bought for $27.
    \nselling price = original price – mark up.
    \nselling price = $30 – $27.
    \nselling price = $3.
    \nso the correct selling price = $3.<\/p>\n

    Question 11.
    \nNate has $50 to spend at the grocery store. He fills his shopping cart with items totaling $46. At checkout he will have to pay 6% sales tax on all items in the cart. Does he have enough money to buy everything in his cart? Explain.<\/p>\n

    Answer:
    \nEnough money to buy everything in his cart = $96.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNate has $50 to spend at the grocery store.
    \nHe fills his shopping cart with items totaling $46.
    \n$50 + $46.
    \n$96.
    \nenough money to buy everything in his cart = $96.<\/p>\n

    Question 12.
    \nA department store buys 300 shirts at a cost of $1,800 and sells them for $10 each. Find the percent markup rounded to the nearest percent.<\/p>\n

    Answer:
    \nThe percent markup = $180.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA department store buys 300 shirts at a cost of $1,800 and sells them for $10 each.
    \nmarkup = percent markup x original price.
    \n$10 = p x $1800.
    \np = $180.
    \nso the percent markup rounded to the nearest percent = $180.<\/p>\n

    Question 13.
    \nMake Sense and Persevere A computer store buys a computer system at a cost of $465.60. The selling price was first at $776, but then the store advertised a 30% markdown on the system.
    \na. Find the current sale price. Round to the nearest cent if necessary.<\/p>\n

    Answer:
    \nThe sales price nearest cent = $310.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA computer store buys a computer system at a cost of $465.60.
    \nThe selling price was first at $776, but then the store advertised a 30% markdown on the system.
    \nsales price = original price – markdown.
    \nsales price = $465.60 – $776.
    \nsales price = 310.4.
    \nso the sales price nearest cent = $310.<\/p>\n

    b. Members of the store’s loyalty club get an additional 10% off their computer purchases. How much do club members pay for the computer with their discount?<\/p>\n

    Answer:<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMembers of the store’s loyalty club get an additional 10% off their computer purchases.<\/p>\n

    Question 14.
    \nHigher Order Thinking<\/strong> A sporting goods store manager was selling a kayak set for a certain price. The manager offered the markdowns shown on the right, making the one-day sale price of the kayak set $328. Find the original selling price of the kayak set.
    \n\"Envision<\/p>\n

    Answer:
    \nThe selling price = $312.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA sporting goods store manager was selling a kayak set for a certain price.
    \nThe manager offered the markdowns shown on the right, making the one-day sale price of the kayak set $328.
    \noriginal selling price = markdown x 40%.
    \nselling price = $328 x 0.4.
    \nselling price = $131.2.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 15.
    \nEliza cannot decide which of two bicycles to buy. The original price of each is $380. The first is marked down by 50%. The second is marked down by 30% with an additional 20% off. Which bicycle should Eliza buy if the bicycles are the same except for the selling price? Explain your answer.<\/p>\n

    Answer:
    \nThe selling price = 0.16.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nEliza cannot decide which of two bicycles to buy.
    \nThe original price of each is $380.
    \nThe first is marked down by 50%.
    \nThe second is marked down by 30% with an additional 20% off.
    \noriginal selling price = markdown x 20%.
    \nselling price = 80% x 0.2.
    \nselling price = 0.16.<\/p>\n

    Question 16.
    \nA shoe store uses a 50% markup for all of the shoes it sells. The store also charges a 10% sales tax on all purchases. What would be the purchase price, including sales tax, of a pair of shoes that has a wholesale cost of $57?<\/p>\n

    Answer:
    \nThe purchase price, including sales tax, of a pair of shoes that has a wholesale cost = $2.28.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA shoe store uses a 50% markup for all of the shoes it sells.
    \nThe store also charges a 10% sales tax on all purchases.
    \nwholesale cost = 40% x $57.
    \nwholesale cost = 0.04 x 57.
    \nwholesale cost = $2.28.<\/p>\n

    Lesson 3.6 Solve Simple Interest Problems<\/h3>\n

    Explore It!<\/strong>
    \nGerard compares the offers at two different banks to decide where he should open a savings account.
    \nI can… apply percent reasoning to solve simple interest problems.
    \n\"Envision<\/p>\n

    A. Draw a representation to show how much would be in the first savings account if Gerard’s initial deposit were d dollars.
    \nAnswer:<\/p>\n

    B. Draw a representation to show how much would be in the second savings account if Gerard’s initial deposit were d dollars.
    \nAnswer:<\/p>\n

    C. Use the two representations you drew to explain how the offers at the two banks are similar and how they are different.
    \nAnswer:<\/p>\n

    Focus on math practices
    \nConstruct Arguments Gerard’s first deposit is $500. Which bank should he choose? Explain.<\/p>\n

    Essential Question<\/strong>
    \nHow does simple interest show proportional reasoning and relate to the percent equation?<\/p>\n

    Try It!<\/strong><\/p>\n

    Victoria has another account at the bank that pays 2\\(\\frac{1}{2}\\)% simple interest. How much interest will she earn in 8 years on an initial deposit of $250 assuming she neither adds to nor withdraws from the account?
    \n2\\(\\frac{1}{2}\\)% interest expressed as a decimal is ________.
    \nInterest after 1 year: s = _______ \u2022 $ _______
    \n= $ _______
    \nInterest after 8 years: $ ______ \u2022 _______
    \n= $ ______
    \nVictoria will earn $ _______ in interest over 8 years.<\/p>\n

    Answer:
    \nThe victoria will earn $2000 in 8 years.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nVictoria has another account at the bank that pays 2\\(\\frac{1}{2}\\)% simple interest.
    \nInterest after 1 year = 1 x 250.
    \nInterest after 8 years = 8 x 250.
    \n2000.
    \nso victoria will earn $2000 in 8 years.<\/p>\n

    Convince Me! Would the interest for the second year be the same if it were calculated on the total after the first year? Why or why not?<\/p>\n

    Try It!<\/strong><\/p>\n

    Another company will lend Maya’s older sister $4,000. Every month, she will pay $11.88 in interest. What is the interest rate, rounded to the nearest tenth of a percent, for 1 year?<\/p>\n

    Answer:
    \nThe interest rate rounded to the nearest tenth of a percent = $3857.44.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAnother company will lend Maya’s older sister $4,000.
    \nEvery month, she will pay $11.88 in interest.
    \n1 year = 12 months.
    \n$11.88 x 12 = $142.56.
    \n4000 – $142.56 = 3857.44.
    \nso the interest rate rounded to the nearest tenth of a percent = $3857.44.<\/p>\n

    Try It!<\/strong><\/p>\n

    Katelyn’s older brother borrowed money for school. He took out a loan that charges 6% simple interest. He will end up paying $720 in interest after 6 years. How much did Katelyn’s brother borrow for school?<\/p>\n

    Answer:
    \nKatelyn’s brother borrows for school = $120.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKatelyn’s older brother borrowed money for school.
    \nHe took out a loan that charges 6% simple interest.
    \nHe will end up paying $720 in interest after 6 years.
    \n$720\/6 = 120.
    \nso Katelyn’s brother borrows for school = $120.<\/p>\n

    KEY CONCEPT<\/strong>
    \nSimple interest represents a proportional relationship between the yearly interest and the principal, or initial amount. The ratio of yearly interest to principal is the interest rate.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How does simple interest show proportional reasoning and relate to the percent equation?<\/p>\n

    Answer:
    \nSimple interest represents a proportional relationship between the yearly interest and the principal or initial amount.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSimple interest represents a proportional relationship between the yearly interest and the principal or initial amount.
    \nthe ratio of yearly interest to principal to the interest rate.<\/p>\n

    Question 2.
    \nReasoning<\/strong> If the interest earned on an account after 2 years is $15, how much would it be after 10 years? Why?<\/p>\n

    Answer:
    \nThe interest earned on an account after 10 years = $60.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIf the interest earned on an account after 2 years is $15.
    \n2 years = $15.
    \n10 years = $15 x $5.
    \n10 years = $60.
    \nso the interest earned on an account after 10 years = $60.<\/p>\n

    Question 3.
    \nBe Precise Angelina is deciding which bank would give her the best simple interest rate on a $300 deposit. One bank says that she will have $320 in her account if she leaves the principal for 2 years. Is this enough information for Angelina to find the interest rate? Explain.<\/p>\n

    Answer:
    \nYes, it is enough information for Angelina to find the interest rate.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAngelina is deciding which bank would give her the best simple interest rate on a $300 deposit.
    \nOne bank says that she will have $320 in her account if she leaves the principal for 2 years.
    \n2 years = 24 months.
    \nfor 1 month = 1 rs.
    \ndo this is enough information.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nFind the missing value in each row. Use the percent equation.
    \n\"Envision<\/p>\n

    Answer:
    \n$15.
    \n4 years.
    \n$50.
    \n1%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n100 x 5\/100 x 3 = $15.
    \n$500 x 4\/100 x 4 = $20.
    \n$50 x 10\/100 x 7 = $35.
    \n$200 x 1\/100 x 2 = $6.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 5.
    \nAnnika’s older cousin borrowed $800 to repair her car. She will pay off the loan after 2 years by paying back the principal plus 4.5% simple interest for each year.
    \na. How much will she pay in interest? Show your work.<\/p>\n

    Answer:
    \nShe will pay = $72.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAnnika’s older cousin borrowed $800 to repair her car.
    \nShe will pay off the loan after 2 years by paying back the principal plus 4.5% simple interest for each year.
    \n800 x 2 x 4.5%.
    \n8 x 2 x 4.5.
    \n$72.
    \nso she will pay = $72.<\/p>\n

    b. How much will she pay back altogether?<\/p>\n

    Answer:
    \nShe will pay back = $72.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAnnika’s older cousin borrowed $800 to repair her car.
    \nShe will pay off the loan after 2 years by paying back the principal plus 4.5% simple interest for each year.
    \n800 x 2 x 4.5%.
    \n8 x 2 x 4.5.
    \n$72.
    \nso she will pay back = $72.<\/p>\n

    Question 6.
    \nJ.D. opened a savings account with $425. After 2 years, the total interest he earned was $10.20. What was the annual interest rate?<\/p>\n

    Answer:
    \nThe annual interest rate = $870.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJ.D. opened a savings account with $425.
    \nAfter 2 years, the total interest he earned was $10.20.
    \n$10.20 + $425 = $435.20.
    \n$435.20 x 2 = $870.4.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7-8, fill in the boxes to solve.
    \nQuestion 7.
    \nEdward deposited $6,000 into a savings account 4 years ago. The simple interest rate is 3%. How much money did Edward earn in interest?
    \nInterest = $ ______ \u2022 ______ \u2022 ______ years
    \nEdward earned $ _______ in interest<\/p>\n

    Answer:
    \nEdward earned = $720.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nEdward deposited $6,000 into a savings account 4 years ago.
    \nThe simple interest rate is 3%.
    \ninterest = $6000 x 4 x 3\/100.
    \ninterest = $60 x 4 x 3.
    \ninterest = $720.
    \nso Edward earned = $720.<\/p>\n

    Question 8.
    \nThe interest on $2,000 for 2 years is $320. What is the simple interest rate?
    \n$ ______ = $2,000 \u2022 r \u2022 ______
    \n$ _____ = $ _____ \u2022 r
    \n______ = r
    \n_______% = r<\/p>\n

    Answer:
    \nThe simple interest rate = 8%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe interest on $2,000 for 2 years is $320.
    \n$320 = $2000 x r x 2.
    \n$320 x 2 = $640.
    \n$640 x $2000 = 8.<\/p>\n

    Question 9.
    \nSuppose you deposited $100 in a savings account 4 years ago with a simple interest rate of 2.2%. The interest that you earned in those 4 years is $8.80. Which of the following is true? Select all that apply.
    \n\u2610 The interest rate is 0.022.
    \n\u2610 The principal was $100.
    \n\u2610 The interest earned is $4.
    \n\u2610 The account was opened 8 years and 8 months ago<\/p>\n

    Answer:
    \nOption B, C, and D are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSuppose you deposited $100 in a savings account 4 years ago with a simple interest rate of 2.2%.
    \nThe interest that you earned in those 4 years is $8.80.
    \nthe principal was $100.
    \nthe interest earned is $4.
    \nthe account was opened 8 years and 8 months ago.<\/p>\n

    Question 10.
    \nA new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.1%.
    \na. How much interest will the customer earn in 20 years?<\/p>\n

    Answer:
    \nThe interest will the customer earn in 20 years = $660.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA new bank customer with $3,000 wants to open a money market account.
    \nThe bank is offering a simple interest rate of 1.1%.
    \n3000 x 11\/1000 x 20.
    \n60 x 11 = 660.
    \nso the interest will the customer earn in 20 years = 660.<\/p>\n

    b. What will be the account balance after 20 years?<\/p>\n

    Answer:
    \nThe interest will the customer earn in 20 years = $660.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA new bank customer with $3,000 wants to open a money market account.
    \nThe bank is offering a simple interest rate of 1.1%.
    \n3000 x 11\/1000 x 20.
    \n60 x 11 = 660.
    \nso the interest will the customer earn in 20 years = 660.<\/p>\n

    Question 11.
    \nBoden’s account has a principal of $500 and a simple interest rate of 3.3%. Complete the double number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
    \n\"Envision<\/p>\n

    Answer:
    \nThe money will be in the account after 4 years = $66.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nBoden’s account has a principal of $500 and a simple interest rate of 3.3%.
    \n$500 x 4 x 3.3.
    \n500 x 4 x 33\/1000.
    \n20 x 3.3 = $66.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Question 12.
    \nCritique Reasoning<\/strong> Monica deposits $100 into a savings account that pays a simple interest rate of 3.4%. Paul deposits $200 into a savings account that pays a simple interest rate of 2.2%. Monica says that she will earn more interest in one year because her interest rate is higher. Do you agree? Justify your response.<\/p>\n

    Answer:
    \nMonica says that she will earn more interest in one year because her interest is higher.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMonica deposits $100 into a savings account that pays a simple interest rate of 3.4%.
    \nPaul deposits $200 into a savings account that pays a simple interest rate of 2.2%.
    \n100 x 3.4 =
    \n34.
    \n200 x 2.2 = 8.8.<\/p>\n

    Question 13.
    \nConstruct Argument<\/strong> Tommy earned $76.00 in interest after 5 years on a principal of $400. Jane earned $82.00 in interest after 2 years on a principal of $1,000. Which bank would you rather use, Tommy’s or Jane’s? Why?<\/p>\n

    Answer:
    \nI will use Jane’s bank.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTommy earned $76.00 in interest after 5 years on a principal of $400.
    \nJane earned $82.00 in interest after 2 years on a principal of $1,000.
    \n400 x 5 x $76 = $152000.
    \n1000 x 82 x 2 = $164000.
    \nJane’s bank will get the higher principal.<\/p>\n

    Question 14.
    \nReasoning<\/strong> A bank manager wants to encourage new customers to open accounts with initial deposits of at least $3,000. He has posters made for the promotion.
    \n\"Envision
    \na. Under the new promotion, what is the minimum amount of interest a new account would make in one year if there were no withdrawls from the account?<\/p>\n

    Answer:
    \nThere were no withdrawals from the account = $144.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA bank manager wants to encourage new customers to open accounts with initial deposits of at least $3,000.
    \nsimple interest of 4.8%.
    \n4.8 x 1 x 3000.
    \n3000 x 48\/1000 x 1.
    \n$144.<\/p>\n

    b. The manager wants to add the sentence, “Open an account with $3,000 and earn at least $120 interest each year!” to the poster. Do you agree? Explain.<\/p>\n

    Answer:
    \nYes, the sentence was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe manager wants to add the sentence, “Open an account with $3,000 and earn at least $120 interest each year!.
    \n4.8 x 1 x 3000.
    \n3000 x 48\/1000 x 1.
    \n$144.
    \nso 144 is greater than $120.
    \nthe sentence was correct.<\/p>\n

    Question 15.
    \nSuppose you deposit $100 in Account A with a simple interest rate of 3.4%, and $300 in Account B with a simple interest rate of 1.8%. One year later, you get a bank statement that shows the interest for Account A is $3.40 and the interest for Account B is $540.00.
    \na. Which account statement is incorrect?<\/p>\n

    Answer:
    \nYes, the account B statement is incorrect.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSuppose you deposit $100 in Account A with a simple interest rate of 3.4%, and $300 in Account B with a simple interest rate of 1.8%.
    \nOne year later, you get a bank statement that shows the interest for Account A is $3.40 and the interest for Account B is $540.00.
    \n3.4 x 100.
    \n34\/1000 x 100.
    \n3.4 x 1.
    \n3.4.
    \n1.8% x 300.
    \n18\/1000 x 300.
    \n1.8 x 3.
    \n5.4.
    \nso the bank statement is incorrect for Account B.<\/p>\n

    b. What may have been the bank’s error?<\/p>\n

    Answer:
    \nThe error is account B.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSuppose you deposit $100 in Account A with a simple interest rate of 3.4%, and $300 in Account B with a simple interest rate of 1.8%.
    \nOne year later, you get a bank statement that shows the interest for Account A is $3.40 and the interest for Account B is $540.00.
    \n3.4 x 100.
    \n34\/1000 x 100.
    \n3.4 x 1.
    \n3.4.
    \n1.8% x 300.
    \n18\/1000 x 300.
    \n1.8 x 3.
    \n5.4.<\/p>\n

    Question 16.
    \nHigher Order Thinking<\/strong> You have two different savings accounts. For Account A, the interest earned after 18 months is $12.00. For Account B, the interest earned after 27 months is $27.00.
    \na. If the interest rate is 3.2% for Account A, how much is the principal?<\/p>\n

    Answer:
    \nThe principle is $6.912.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nYou have two different savings accounts.
    \nFor Account A, the interest earned after 18 months is $12.00.
    \nFor Account B, the interest earned after 27 months is $27.00.
    \n$12 x 18 x 3.2%.
    \n$12 x 18 x 0.032.
    \n$12 x 0.576.
    \n$6.912.<\/p>\n

    b. If the interest rate is 2.4% for Account B, how much is the principal?<\/p>\n

    Answer:
    \nThe principle is $17.496.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nYou have two different savings accounts.
    \nFor Account A, the interest earned after 18 months is $12.00.
    \nFor Account B, the interest earned after 27 months is $27.00.
    \n27 x $27 x 0.024.
    \n$27 x 0.648.
    \n17.496.<\/p>\n

    c. Which account earned you the most interest in the first year? Explain.<\/p>\n

    Answer:
    \nAccount B has earned the most interest in the first year.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nYou have two different savings accounts.
    \nFor Account A, the interest earned after 18 months is $12.00.
    \nFor Account B, the interest earned after 27 months is $27.00.
    \n27 x $27 x 0.024.
    \n$27 x 0.648.
    \n17.496.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 17.
    \nA certificate of deposit with principal $150 earns 4% annual interest for 2 years. Select all the options that would earn the same amount of interest.
    \n\u2610 $300 at 2% for 2 years
    \n\u2610 $150 at 6% for 18 months
    \n\u2610 $400 at 3% for 1 year
    \n\u2610 $100 at 1% for 8 years
    \n\u2610 $50 at 48% for 6 months<\/p>\n

    Answer:
    \nOption A and option C are correct.<\/p>\n

    Explanation:
    \nIn the above-given given question,
    \ngiven that,
    \nA certificate of deposit with a principal of $150 earns 4% annual interest for 2 years.
    \n$150 x 4% x 2.
    \n$150 x 4\/100 x 2.
    \n$15 x 0.4 x 2.
    \n$12.
    \nso option A and option C are correct.<\/p>\n

    Question 18.
    \nDakota earned $15.75 in interest in Account A and $28.00 in interest in Account B after 21 months. If the simple interest rate is for 3.0% for Account A and 4.0% for Account B, which account had the greater principal? Explain.<\/p>\n

    Answer:
    \nAccount B had the greater principal.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDakota earned $15.75 in interest in Account A and $28.00 in interest in Account B after 21 months.
    \nIf the simple interest rate is 3.0% for Account A and 4.0% for Account B, which account had the greater principal.
    \n$15.75 x 3% x 21.
    \n15.75 x 0.003 x 21.
    \n0.99225.
    \n$28 x 21 x 4%.
    \n$28 x 21 x 0.04.
    \n$23.52.
    \nso account B had the greater principal.<\/p>\n

    Topic 3 Review<\/h3>\n

    Topic Essential Question<\/strong>
    \nHow can percents show proportional relationships between quantities and be used to solve problems?<\/p>\n

    Vocabulary Review<\/strong>
    \nComplete each definition and then provide an example of each word.
    \n\"Envision<\/p>\n

    Answer:
    \n1: Markup simple interest.
    \n2: Percent change.
    \n3: Markup principal.
    \n4: Vocabulary.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe markup simple interest is the decrease from the original price of an item to its sale price.
    \nthe accuracy of a measured or estimated value compared to its actual value is described as the percent change.
    \nan initial amount of money that is deposited in an account is called the markup principal.
    \nthe vocabulary describes how much a quantity has changed relative to its original amount.
    \n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-3-Analyze<\/p>\n

    Use Vocabulary in Writing
    \nBirute deposits $500 in a savings account with a simple interest rate of 1.3%. How could you use this information to find the interest she would earn in 4 years and determine the percent change in her savings account?<\/p>\n

    Answer:
    \nThe percent change in her savings account.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nBirute deposits $500 in savings account with a simple interest rate of 1.3%
    \nHow could you use this information to find the interest she would earn in 4 years and determine the percent change.
    \n$500 x 1.3% x 4.
    \n$500 x 13\/1000 x 4.
    \n5 x 1.3 x 4.
    \n26.
    \nso the percent change in her savings account.<\/p>\n

    Concepts and Skills Review<\/strong><\/p>\n

    Lesson 3.1 Analyze Percents of Numbers<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou can use equivalent ratios to find the percent of a number. Remember that a percent is a ratio that relates a number to 100.<\/p>\n

    Example<\/strong>
    \nFind 57% of 690.
    \n\\(\\frac{57}{100}=\\frac{x}{690}\\)
    \n\\(\\frac{57}{100} \\cdot 690=\\frac{x}{690} \\cdot 690\\)
    \n393.3 = x<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nFind 0.8% of 1,046.<\/p>\n

    Answer:
    \n8.368.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n0.8% of 1046.
    \n0.8\/100 x 1046.
    \n0.008 x 1046.
    \n8.368.<\/p>\n

    Question 2.
    \nFind 160% of 98.<\/p>\n

    Answer:
    \n156.8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n160% of 98.
    \n160\/100 x 98.
    \n1.6 x 98.
    \n156.8.<\/p>\n

    Question 3.
    \nA company charges a shipping fee that is 4.5% of the purchase price for all items it ships. What is the fee to ship an item that costs $56?<\/p>\n

    Answer:
    \nThe fee to ship an item that costs = $2.52.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \ncompany charges a shipping fee that is 4.5% of the purchase price for all items it ships.
    \n$56 x 4.5%.
    \n56 x 45\/1000.
    \n$56 x 0.045.
    \n$2.52.<\/p>\n

    Lesson 3.2 Connect Percent and Proportion<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou can use proportions to solve different types of percent problems. There are three values in a percent problem–the percent, the part, and the whole. If you know two of these values, you can set up a proportion to find the third value.<\/p>\n

    Example<\/strong>
    \nWhat percent of 19 is 4.75?
    \nThe whole is 19 and the part is 4.75. Write a proportion, and solve for the percent, p.
    \n\\(\\frac{\\text { part }}{\\text { whole }}=\\frac{p}{100}\\)
    \n\\(\\frac{4.75}{19}=\\frac{p}{100}\\)
    \n\\(\\frac{4.75}{19} \\cdot 100=\\frac{p}{100} \\cdot 100\\)
    \n25 = p
    \nSo, 4.75 is 25% of 19.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \n24.94 is 29% of what number?<\/p>\n

    Answer:
    \nThe number is 7.3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n24.94 is 29% of what number.
    \n24.94 \/ p = 29\/100.
    \np = 0.29 x 24.94.
    \np = 7.3.<\/p>\n

    Question 2.
    \nOn Thursday, a restaurant serves iced tea to 35 of its 140 customers. What percent of the customers order iced tea?<\/p>\n

    Answer:
    \nThe percent of the customers who order iced tea = 25%.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOn Thursday, a restaurant serves iced tea to 35 of its 140 customers.
    \n35\/140 = p\/100.
    \n0.25 x 100 = p.
    \np = 25%.<\/p>\n

    Question 3.
    \nLiam puts $40 in savings in March and 175% of this amount in savings in April. How much does Liam put in savings in April?<\/p>\n

    Answer:<\/p>\n

    whole = 100
    \n4,75 = 100 4,175. 100 = 70100<\/p>\n

    Lesson 3.3 Represent and Use the Percent Equation<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou can use the percent equation to solve percent problems.
    \npart = percent \u2022 whole
    \nSubstitute two of the three values to solve for the unknown value.<\/p>\n

    Example<\/strong>
    \nMichael earns a 6% commission on each house he sells. If he sells a house for $180,000, how much does he earn in commission, c?
    \nc = 0.06. 180,000
    \nc = 10,800
    \nMichael earns $10,800 in commission.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nSharon paid $78 sales tax on a new camera. If the sales tax rate is 6.5%, what was the cost of the camera?<\/p>\n

    Answer:<\/p>\n

    Question 2.
    \nThere are 45 students who play a woodwind instrument in the school band. Of these, 18 play the saxophone. What percent of these students play the saxophone?
    \nAnswer:<\/p>\n

    Lesson 3.4 Solve Percent Change and Percent Error Problems<\/strong><\/p>\n

    Quick Review<\/strong>
    \nA percent change can be an increase or a decrease. You can use an equation to find a percent change.
    \nchange = percent change \u2022 original amount
    \nA percent error is always a nonnegative value. You can use an equation to find a percent error.
    \ndifference = percent error \u2022 actual<\/p>\n

    Example<\/strong>
    \nJuan’s puppy weighed 16 pounds at the age of 2 months. The puppy weighed 60 pounds at the age of 8 months. What is the percent change in the puppy’s weight?
    \nchange in pounds = 60 \u2013 16 = 44
    \n44 = P \u2022 16
    \n\\(\\frac{44}{16}\\) = P
    \n2.75 = P
    \nThe puppy’s weight increased by 275%.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nIn 2014, the attendance at Jefferson School’s Fall Festival was 650. In 2015, the attendance was 575. What was the percent change in attendance from 2014 to 2015? Round to the nearest whole percent.
    \nAnswer:<\/p>\n

    Question 2.
    \nMelissa estimated that she would read 250 pages last week. She read 290 pages. What is the percent error of Melissa’s estimate? Round to the nearest whole percent.
    \nAnswer:<\/p>\n

    Lesson 3.5 Solve Markup and Markdown Problems<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou can use the percent equation to solve markup and markdown problems.
    \nmarkup = percent markup \u2022 cost
    \nmarkdown = percent markdown \u2022 selling price<\/p>\n

    Example<\/strong>
    \nBree buys a purse for $90. She sells it at her store for $135. What is the percent markup on the purse?
    \nmarkup = $135 \u2013 $90 = $45
    \n45 = P \u2022 90
    \n45 = P
    \n0.5 =P The decimal 0.5 is equivalent to 50%.
    \nThe percent markup on the purse is 50%.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nHank buys a used car for $7,200 and plans to sell it on his used car lot. What is the price of the car after a markup of 15%?<\/p>\n

    Answer:
    \nThe price of the car after a markup of 15% =<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHank buys a used car for $7,200 and plans to sell it on his used car lot.
    \npart = percent x whole.
    \npart = 15 x 7200.
    \npart = 15\/100 x 7200.
    \npart = 1080.
    \nso the price of the car after a markup of 15% = 1080.<\/p>\n

    Question 2.
    \nNya wants to buy a sweater that had an original price of $55. The sweater is now discounted 20% and the sales tax rate is 5.5%. How much will Nya pay for the sweater?<\/p>\n

    Answer:
    \nNya pays for the sweater.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nNya wants to buy a sweater that had an original price of $55.
    \nThe sweater is now discounted 20% and the sales tax rate is 5.5%.
    \n$55 x 20\/100 x 5.5%.
    \n55 x 0.2 x 55\/1000.
    \n55 x 0.2 x 0.055.
    \n0.605.
    \nso Nya pays for the sweater = 0.605.<\/p>\n

    Lesson 3.6 Solve Simple Interest Problems<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou consider four quantities when solving problems involving simple interest.
    \ninitial amount, or principal, p
    \ninterest rate, r
    \ntime, t amount of simple interest, I<\/p>\n

    Example<\/strong>
    \nYuni loaned $400 to her brother. He will repay the loan by paying 2.5% simple interest for 3 years. How much will he pay in interest?
    \nI = 400 \u2022 0.025 \u2022 3 = $30
    \nHe will pay $30 in interest.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nEthan put $700 into a Certificate of Deposit (CD) account that earns 1.8% interest each year. What will the interest of the CD account be after 6 years?<\/p>\n

    Answer:
    \nThe interest of the CD account is after 6 years = $75.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nEthan put $700 into a Certificate of Deposit (CD) account that earns 1.8% interest each year.
    \n$700 x 1.8% x 6.
    \n$700 x 1.8\/100 x 6.
    \n$700 x 0.018 x 6.
    \n$75.6.<\/p>\n

    Question 2.
    \nKelly opened a bank account that earns 1.2% simple interest each year. After 7 years, Kelly will earn $126 in interest. How much did Kelly deposit when she opened the account?<\/p>\n

    Answer:
    \nThe kelly deposit when she opened the account = $10.584.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKelly opened a bank account that earns 1.2% simple interest each year.
    \nAfter 7 years, Kelly will earn $126 in interest.
    \n$126 x 7 x 1.2%.
    \n$126 x 7 x 1.2\/100.
    \n$126 x 7 x 0.012.
    \n$126 x 0.084.
    \n$10.584.
    \nso the kelly deposit when she opened the account = $10.584.<\/p>\n

    Topic 3 Fluency Practice<\/h3>\n

    Riddle Rearranging<\/strong>
    \nFind the value of x in each unit rate. Then arrange the answers in order from least to greatest. The letters will spell out the answer to the riddle below.
    \nI can… find unit rates with ratios of fractions.
    \n\"Envision<\/p>\n

    Answer:
    \n0.75 xc = 0.3h, 0.4 min = 0.6 ml, and 0.25 mi = 0.625 h.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3\/4c\/1\/3h = xc\/1h.
    \n0.75c\/0.3h = xc\/h.
    \n0.75c x xc = 0.3h x h.
    \n0.75xc = 0.3h.
    \n3\/5ml\/2\/5 min = x ml \/1min.
    \n0.6ml\/0.4 min = x ml \/ 1 min.
    \n0.4 x 1 min = x ml x 0.6 ml.
    \n0.4 min = 0.6ml.
    \n1\/4mi\/5\/8 h = x mi \/ 1h.
    \n0.25 mi\/ 0.625 h = x mi \/ 1h.
    \nx mi \/1 h = 0.25 mi\/0.625 h.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Go through the\u00a0enVision Math Common Core Grade 7 Answer Key\u00a0Topic 3 Analyze And Solve Percent Problems\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 7th Grade Answers Key Topic 3 Analyze And Solve Percent Problems Topic 3 Essential Question How can percents show proportional relationships between quantities and be used to solve …<\/p>\n","protected":false},"author":1,"featured_media":25563,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/09\/Envision-Math-Common-Core-Grade-7-Answer-Key-Topic-3-Analyze-And-Solve-Percent-Problems.png","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/14769"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=14769"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/14769\/revisions"}],"predecessor-version":[{"id":28240,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/14769\/revisions\/28240"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media\/25563"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=14769"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=14769"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=14769"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}