3.1 Use a Problem-Solving Strategy

A repeatable routine for turning a word problem into an equation, practiced on number and consecutive-integer problems.

Elementary Algebra 2e, 3.1 Use a Problem-Solving Strategy

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59 exercises

3.1 Exercise 1

Before you get started, take this readiness quiz.

Translate “6 less than twice x” into an algebraic expression.
If you missed this problem, review the reference.

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3.1 Exercise 2

Solve: $\frac{2}{3} x = 24 .$
If you missed this problem, review the reference.

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3.1 Exercise 3

Solve: $3 x + 8 = 14 .$
If you missed this problem, review the reference.

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3.1 Exercise 5

Joaquin bought a bookcase on sale for $120, which was two-thirds of the original price. What was the original price of the bookcase?

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3.1 Exercise 6

Two-fifths of the songs in Mariel’s playlist are country. If there are 16 country songs, what is the total number of songs in the playlist?

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3.1 Exercise 8

Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was 3 more than twice the number of notebooks. He bought 7 textbooks. How many notebooks did he buy?

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3.1 Exercise 9

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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3.1 Exercise 11

The difference of a number and eight is 17. Find the number.

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3.1 Exercise 12

The difference of a number and eleven is $−7 .$ Find the number.

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3.1 Exercise 14

The sum of four times a number and two is 14. Find the number.

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3.1 Exercise 15

The sum of three times a number and seven is 25. Find the number.

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3.1 Exercise 17

One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.

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3.1 Exercise 18

The sum of two numbers is fifty-eight. One number is four more than the other. Find the numbers.

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3.1 Exercise 20

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

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3.1 Exercise 21

The sum of two numbers is $−18 .$ One number is 40 more than the other. Find the numbers.

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3.1 Exercise 23

One number is eight more than twice another. Their sum is negative four. Find the numbers.

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3.1 Exercise 24

One number is three more than three times another. Their sum is $−5 .$ Find the numbers.

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3.1 Exercise 26

The sum of two consecutive integers is $95 .$ Find the numbers.

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3.1 Exercise 27

The sum of two consecutive integers is $−31 .$ Find the numbers.

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3.1 Exercise 29

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

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3.1 Exercise 30

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

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3.1 Exercise 31

Find three consecutive even integers whose sum is 84.

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3.1 Exercise 32

Find three consecutive even integers whose sum is 102.

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3.1 Exercise 33

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

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3.1 Exercise 35

According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,500. This was $1,500 less than 6 times the cost in 1975. What was the average cost of a car in 1975?

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3.1 Exercise 36

U.S. Census data shows that the median price of new home in the United States 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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3.1 Exercise 37

Prepare the lists described.

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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3.1 Exercise 39

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

Two-thirds of the children in the fourth-grade class are girls. If there are 20 girls, what is the total number of children in the class?

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3.1 Exercise 41

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

Zachary has 25 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?

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3.1 Exercise 43

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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3.1 Exercise 45

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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3.1 Exercise 47

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

Philip pays $1,620 in rent every month. This amount is $120 more than twice what his brother Paul pays for rent. How much does Paul pay for rent?

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3.1 Exercise 49

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

Laurie has $46,000 invested in stocks and bonds. The amount invested in stocks is $8,000 less than three times the amount invested in bonds. How much does Laurie have invested in bonds?

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