Practice questions available in **McGraw Hill Math Grade 6 Answer Key PDF Lesson 9.5 Problem-Solving with Proportions** will engage students and is a great way of informal assessment.

## McGraw-Hill Math Grade 6 Answer Key Lesson 9.5 Problem-Solving with Proportions

**Exercises Solve For x**

Question 1.

If a car can travel 105 miles on 7 gallons of gas, how far can it travel on 9 gallons of gas?

Answer:

Number of miles a car can it travel on 9 gallons of gas = 135.

Explanation:

Number of miles car can travel = 105.

Number of gallons of gas = 7.

Number of miles a car can it travel on 9 gallons of gas =

105 miles – 7 gallon of gas

?? miles – 9 gallon of gas

=> 105 × 9 = 7 × ??

=> 945 ÷ 7 = ??

=> 135 = ??

Question 2.

Isabella runs 3 times per week. She ran for 15 minutes on Monday and 17 minutes on Wednesday. Her coach told her that she had run 80 percent of her goal that week. How many more minutes does she need to run to meet her goal for the week?

Answer:

Number of minutes she needs to run to meet her goal for the week = 8.

Explanation:

Number of times Isabella runs per week = 3.

Number of minutes she ran on Monday = 15.

Number of minutes she ran on Wednesday = 17.

Her coach told her that she had run 80 percent of her goal that week

=> Let the total minutes she ran be x.

80% of x = 15 + 17

=> 80% of x = 32

=> 80x = 3200

=> x = 3200 ÷ 80

=> x = 40.

Number of minutes she needs to run to meet her goal for the week = Total number of minutes she ran – (Number of minutes she ran on Monday + Number of minutes she ran on Wednesday)

= 40 – (15 + 17)

= 40 – 32

= 8.

Question 3.

It takes Kenny 25 minutes to inflate the tires of 55 bicycles. How long will it take him to inflate the tires of 121 bicycles?

Answer:

Number of minutes it takes him to inflate the tires of 121 bicycles = 55.

Explanation:

Number of minutes to inflate the tires Kenny takes = 25.

Number of bicycles Kenny takes to inflate the tires = 55.

Number of minutes it takes him to inflate the tires of 121 bicycles =

25 minutes – 55

?? minutes – 121

=> 121 × 25 = 55 × ??

=> 3,025 ÷ 55 = ??

=> 55 minutes = ??.

Question 4.

How many pizzas do you need for a party of 135 people if at the last party. 90 people ate 52 pizzas? (Assume the same rate of consumption.)

Answer:

Number of pizzas 135 people ate = 78.

Explanation:

Number of people = 90.

Number of pizzas = 52.

Number of pizzas 135 people ate =

90 people – 52 pizzas

135 people – ??

=> 90 × ?? = 135 × 52

=> ?? = 7,020 ÷ 90

=> ?? = 78.

Question 5.

Jim spent $55 at the last yard sale when he bought 14 items. If he sees 24 items that he liked at the yard sale across the street, how much money should he expect to spend? (Assume he spends the same amount per item.)

Answer:

Amount of money Jim should he expect to spend = $94.28.

Explanation:

Amount of money Jim spent at the last yard sale = $55.

Number of items he bought = 14.

Number of items yard sale across the street = 24.

Amount of money Jim should he expect to spend =

$55 – 14 items

$?? – 24 items

=> 55 × 24 = 14 × ??

=> 1,320 ÷ 14 = ??

=> $94.28 = ??

Question 6.

Kim wants to expand her lawn mowing business. She presently mows 58 lawns with 6 workers. how many workers will she need if she plans to mow a total of 87 lawns?

Answer:

Number of workers will she needs if she plans to mow a total of 87 lawns = 9.

Explanation:

Number of workers = 6.

Number of lawns she presently mows = 58.

Number of workers will she needs if she plans to mow a total of 87 lawns =

6 workers – 58 lawns

?? workers – 87 lawns

=> 87 × 6 = 58 × ??

=> 522 ÷ 58 = ??

=> 9 workers = ??.

Question 7.

At the apple orchard, each row of 7 apple trees yields 78 bushels of apples. If there are 112 trees in the orchard, how many bushels of apples should you expect to be harvested?

Answer:

Number of bushels of apples should you expect to be harvested = 1,248 bushels of apples.

Explanation:

Number of apples trees yields in each row = 7.

Number of bushels of apples = 78.

Number of bushels of apples should you expect to be harvested =

7 apple trees – 78 bushels of apples

112 apple trees – ?? bushels of apples

=> 7 × ?? = 78 × 112

=> ?? = 8,736 ÷ 7

=> ?? = 1,248 bushels of apples.

Question 8.

Each troop of 32 girl scouts eats 11 pounds of cereal a week. If there are 45 troops at the scout camp, how many pounds of cereal should be purchased?

Answer:

Number of pounds of cereal should be purchased = 15.46.

Explanation:

Number of each troop has = 32.

Number of pounds of cereal a week girl scouts eats = 11.

Number of troops at the scout camp = 45.

Number of pounds of cereal should be purchased =

32 troop – 11 pounds of cereal

45 troop – ?? pounds of cereal

=> 32 × ?? = 11 × 45

=> ?? = 495 ÷ 32

=> ?? = 15.46 pounds of cereal.