2.2 Use a Problem Solving Strategy

Turning word problems into equations with a step-by-step method, applied to number puzzles, percent change, and simple interest.

Intermediate Algebra 2e, 2.2 Use a Problem Solving Strategy

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78 exercises

2.2 Exercise 1

Before you get started, take this readiness quiz.

Translate “six less than twice x” into an algebraic expression.
If you missed this problem, review the reference.

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2.2 Exercise 2

Convert 4.5% to a decimal.
If you missed this problem, review the reference.

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2.2 Exercise 3

Convert 0.6 to a percent.
If you missed this problem, review the reference.

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2.2 Exercise 5

Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was three more than twice the number of notebooks. He bought seven textbooks. How many notebooks did he buy?

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2.2 Exercise 6

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?

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2.2 Exercise 8

The sum of four times a number and two is fourteen. Find the number.

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2.2 Exercise 9

The sum of three times a number and seven is twenty-five. Find the number.

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2.2 Exercise 11

The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.

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2.2 Exercise 12

The sum of two numbers is negative eighteen. One number is forty more than the other. Find the numbers.

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2.2 Exercise 14

Find three consecutive integers whose sum is $−96 .$

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2.2 Exercise 15

Find three consecutive integers whose sum is $−36 .$

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2.2 Exercise 16

Find three consecutive even integers whose sum is $120$ .

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2.2 Exercise 17

Find three consecutive even integers whose sum is 102.

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2.2 Exercise 18

Find three consecutive even integers whose sum is $−24 .$

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2.2 Exercise 19

A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. What does the husband earn?

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2.2 Exercise 20

According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,400. This was $1,600 less than six times the cost in 1975. What was the average cost of a car in 1975?

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2.2 Exercise 21

US Census data shows that the median price of new home in the U.S. in November 2014 was $280,900. This was $10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?

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2.2 Exercise 23

Translate and solve: ⓐ What number is 45% of 80? ⓑ 7.5% of what amount is $1.95? ⓒ 110 is what percent of 88?

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2.2 Exercise 24

Translate and solve: ⓐ What number is 55% of 60? ⓑ 8.5% of what amount is $3.06? ⓒ 126 is what percent of 72?

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2.2 Exercise 26

One serving of wheat square cereal has 7 grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber?

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2.2 Exercise 27

One serving of rice cereal has 190 mg of sodium, which is 8% of the recommended daily amount. What is the total recommended daily amount of sodium?

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2.2 Exercise 29

Mitzi received some gourmet brownies as a gift. The wrapper said each brownie was 480 calories, and had 240 calories of fat. What percent of the total calories in each brownie comes from fat? Round the answer to the nearest whole percent.

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2.2 Exercise 30

The mix Ricardo plans to use to make brownies says that each brownie will be 190 calories, and 76 calories are from fat. What percent of the total calories are from fat? Round the answer to the nearest whole percent.

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2.2 Exercise 32

Find the percent change. (Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to 55.5 cents from 51 cents.

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2.2 Exercise 33

Find the percent change. (Round to the nearest tenth of a percent.) In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was 2.25.

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2.2 Exercise 35

Find ⓐ the amount of mark-up and ⓑ the list price: Jim’s music store bought a guitar at original cost $1,200. Jim marked the price up 50%.

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2.2 Exercise 36

Find ⓐ the amount of mark-up and ⓑ the list price: The Auto Resale Store bought Pablo’s Toyota for $8,500. They marked the price up 35%.

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2.2 Exercise 37

Areli invested a principal of $950 in her bank account that earned simple interest at an interest rate of 3%. How much interest did she earn in five years?

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2.2 Exercise 38

Nathaly deposited $12,500 in her bank account where it will earn 4% simple interest. How much interest will Nathaly earn in five years?

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2.2 Exercise 39

Susana invested a principal of $36,000 in her bank account that earned simple interest at an interest rate of $6.5 \% .$ How much interest did she earn in three years?

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2.2 Exercise 40

Hang borrowed $7,500 from her parents to pay her tuition. In five years, she paid them $1,500 interest in addition to the $7,500 she borrowed. What was the rate of simple interest?

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2.2 Exercise 41

Jim lent his sister $5,000 to help her buy a house. In three years, she paid him the $5,000, plus $900 interest. What was the rate of simple interest?

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2.2 Exercise 42

Loren lent his brother $3,000 to help him buy a car. In four years, his brother paid him back the $3,000 plus $660 in interest. What was the rate of simple interest?

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2.2 Exercise 43

Sean’s new car loan statement said he would pay $4,866.25 in interest from a simple interest rate of 8.5% over five years. How much did he borrow to buy his new car?

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2.2 Exercise 44

Eduardo noticed that his new car loan papers stated that with a 7.5% simple interest rate, he would pay $6,596.25 in interest over five years. How much did he borrow to pay for his car?

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2.2 Exercise 45

In five years, Gloria’s bank account earned $2,400 interest at 5% simple interest. How much had she deposited in the account?

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2.2 Exercise 46

Use a Problem Solving Strategy for Word Problems

List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.

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2.2 Exercise 48

Solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.

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2.2 Exercise 50

Solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

Huong is organizing paperback and hardback books for her club’s used book sale. The number of paperbacks is 12 less than three times the number of hardbacks. Huong had 162 paperbacks. How many hardback books were there?

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