## Envision Math 6th Grade Textbook Answer Key Topic 2.8 Problem Solving

Problem Solving

Make a Table
The Douglas family had $700 in their road-trip fund. They spent$75 each day on their trip. If x equals the number of days, write an expression that describes the amount of money left in the fund after x days.

Question.
Make a table to show the values of the expression for x = 3 days, x = 5 days, and x = 9 days.

Guided Practice

Do you know HOW?
Question 1.
The sixth-grade chess club is washing cars for a fund-raiser. They started with $150 in their fund and are charging$5 per car. Use the expression 150 + 5x to copy and complete the table, to find how much money the chess club will have after washing 25, 31, and 54 cars.

Do you UNDERSTAND?
Question 2.
How do you know what labels to use in a table?

Question 3.
Write a Problem Use the table to write a word problem that could be solved using the table below.

Independent Practice

Question 4.
For every A Josh earns on his report card, he is given 2 movie passes. He still has 2 movie passes left from his last report card. If x equals the number of A’s Josh earns, use the expression 2x + 2 to copy and complete the table to find how many movie passes Josh will have for 1,2, or 3 A’s.

Plan and Solve
Write an expression that describes the amount of money left in the fund after x days.

Total in fund – $75(number of days) 700 – 75x Plan and Solve Make a table to solve for different values of x. Include labels for the variable and the expression. Enter the values of x you want to find. Then solve the expression for each value. Question 5. Kat is playing a game called “500.” Each player starts with 500 points and loses 10 points for each question answered correctly. The first player to reach 0 points wins. Which expression represents how many points Kat will have if she answers x questions correctly? A. 500x B. 500 – 10x C. 500 + 10x D. 10x – 500 Answer: B. 500 – 10x Explanation: Question 6. Copy and complete the table for Exercise 5 to find how many points Kat will have if she answers 9, 13, and 24 questions correctly. Answer: Explanation: Question 7. Jordan is playing in a charity basketball game. The local barber pledged to pay$2 for every point he scores. The local grocery store will give a one-time donation of $75. Which expression represents how much money Jordan will raise if he scores x points? A. 75 + 2x B. 77x C. 75 + 4x D. 75 – 2x Answer: A. 75 + 2x Explanation: Question 8. Jeremy started a club to help senior citizens use computers. On the first day, he was the only member. On the second day, two friends joined. Each day after that, two more members joined. If x equals the number of days, evaluate the expression 1 + 2(x – 1) to find the membership of the club on the 10th day. Answer: 19 people Explanation: Question 9. The camp chef is making waffles for breakfast. The recipe calls for 3 cups of milk for every batch. If x equals the number of batches, copy and complete the table to show how much milk the chef needs for 3, 7, and 10 batches. Answer: Explanation: Independent Practice Use the information at right for 10 through 14. Question 10. Carver bought some plants at the Garden Center sale. On his bill, he saw that he had paid$20 for 5 plants. What size did Carver buy?
He bought 5 large plants.
Explanation:

Question 11.
Sally and her mother went to the sale at the Garden Center. Sally bought x large plants and y small plants. She paid with a twenty-dollar bill. Make a table using the expression 20 – (4x + 2y) to show how much change she received if she bought 2 large plants and 4 small plants; 4 large plants and 2 small plants; or 1 large plant and 7 small plants.
See margin.
Explanation:

Tips: Make a separate column for each variable.
Question 12.
Elyse has a small flower garden in her backyard. She wants to plant seven rows of flowers. She drew a plan of her garden.

a. If each row can hold 3 large plants, 4 medium plants, or 8 small plants, how many of each should Elyse buy?
See margin.
Explanation:

b. What will the total cost be for all of Elyse’s plants?
$100 Explanation: Question 13. Maggie wants to plant a 10 ft row of large plants. A large plant needs 1.5 ft between plants. Maggie will put her first plant 0.5 ft in from the end. How much money will Maggie need to fill the row? Explain how you found your answer. Answer:$28; sample answer; I drew a picture to show 7 plants.
Explanation:

Question 14.
Art has $32. How many large plants could he buy? Medium plants? Small plants? Answer: 8 large; 10 medium; 16 small Explanation: Think About the Process Question 15. William and Anne are selling magazines. For each magazine sold, their soccer team raises$2.25. Which value completes this table?

A. 19.25
B. 382.5
C. 3825
D. 38.25
D. 38.25

Question 16.
Tanya has a job delivering newspapers. Every week, her customers pay her $1.50. She also receives an allowance of$5 a week. If Tanya has x newspaper clients, which expression best describes how much money Tanya receives each week?
A. 5x – 1.5
B. 5x + 1.5
C. 5 + 1.5x
D. 5 – 1.5x

Stop and Practice

Skills Review Write each phrase as an algebraic expression.
Question 1.
7 less than a number x

Question 2.
5 times a number p

Question 3.
4 times a number m, minus 3 times a number k

Question 4.
8 plus two times a number j

Use the properties of operations to fill in the blanks in each expression.
Question 5.
28 × 5 = 5 × ☐

Question 6.
12 × 25 × 32 = 12 × ☐ × 25 × 32

Question 7.
7 + (30 + 15) = (7 + 30) + ☐

Question 8.
23 + 8 = 23 + 8 + ☐

Evaluate each expression for x = 3 and y = 5.
Question 9.
5x + 8

Question 10.
(10 – y) (10)

Question 11.
10y + 23

Question 12.
Write an algebraic expression for the value of y that explains the relationship between x and y. Then finish the table.

Error Search Find each answer that is not correct. Write it correctly and explain the error.
Question 13.
8 + 2 × 6 = 60

Question 14.
8 × 0 + (4 × 1) = 4

Question 15.
4(24) = 4(6) + 4(4)

Question 16.
32 + 73 = (30 + 70) + (2 + 3)

Question 17.
58(40) = 50(40) × 8(40)

Question 18.
4(51 + 32) = 4(80) + 4(3)

Number Sense

Insert parentheses to make each sentence true.
Question 19.
3 × 8 + 3 × 2 = 66

Question 20.
2 × 5 + 4 – 8 = 10

Question 21.
15 – 2 × 3 + 52 = 64

Question 22.
4x – 5 = 4x – 20

Question 23.
6 + 8 – 3 × 7 = 41

Question 24.
4 + 4 × 3 + 5 = 29