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9.1 Use a Problem Solving Strategy

Naming the unknown, translating a sentence into an equation, and checking the answer against the wording, drilled on number and consecutive-integer puzzles.

Prealgebra 2e, 9.1 Use a Problem Solving Strategy

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48 exercises

9.1 Exercise 1

Before you get started, take this readiness quiz.

Translate “6\text{``}\text{6} less than twice x”\textit{x} \" into an algebraic expression.
If you missed this problem, review the reference.

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9.1 Exercise 2

Solve: 23x=24.\frac{2}{3} x = 24 .
If you missed this problem, review the reference.

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9.1 Exercise 3

Solve: 3x+8=14.3 x + 8 = 14 .
If you missed this problem, review the reference.

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9.1 Exercise 5

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

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9.1 Exercise 6

Two-fifths of the people in the senior center dining room are men. If there are 1616 men, what is the total number of people in the dining room?

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9.1 Exercise 8

Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was 33 more than the number of notebooks. He bought 55 textbooks. How many notebooks did he buy?

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9.1 Exercise 9

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is seven more than the number of crossword puzzles. He completed 1414 Sudoku puzzles. How many crossword puzzles did he complete?

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9.1 Exercise 11

Pilar's rent increased by 4%.\text{4}\% . The increase was $38.\$\text{38} . What was the original amount of Pilar's rent?

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9.1 Exercise 12

Steve saves 12%\text{12}\% of his paycheck each month. If he saved $504\$\text{504} last month, how much was his paycheck?

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9.1 Exercise 14

The difference of a number and eight is 17.17 . Find the number.

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9.1 Exercise 15

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

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9.1 Exercise 17

The sum of four times a number and two is 14.14 . Find the number.

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9.1 Exercise 18

The sum of three times a number and seven is 25.25 . Find the number.

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9.1 Exercise 20

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

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9.1 Exercise 21

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

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9.1 Exercise 23

The sum of two numbers is negative twenty-three. One number is 77 less than the other. Find the numbers.

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9.1 Exercise 24

The sum of two numbers is negative eighteen. One number is 4040 more than the other. Find the numbers.

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9.1 Exercise 26

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

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9.1 Exercise 27

One number is three more than three times another. Their sum is negative five. Find the numbers.

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9.1 Exercise 29

The sum of two consecutive integers is 95.95 . Find the numbers.

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9.1 Exercise 30

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

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9.1 Exercise 32

Find three consecutive integers whose sum is 96.96 .

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9.1 Exercise 33

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

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9.1 Exercise 34

Use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Two-thirds of the children in the fourth-grade class are girls. If there are 2020 girls, what is the total number of children in the class?

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9.1 Exercise 36

Use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Zachary has 2525 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?

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9.1 Exercise 38

Use the problem-solving strategy for word problems to solve. Answer in complete sentences.

There are 1616 girls in a school club. The number of girls is 44 more than twice the number of boys. Find the number of boys in the club.

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9.1 Exercise 40

Use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Lee is emptying dishes and glasses from the dishwasher. The number of dishes is 88 less than the number of glasses. If there are 99 dishes, what is the number of glasses?

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9.1 Exercise 42

Use the problem-solving strategy for word problems to solve. Answer in complete sentences.

After 33 months on a diet, Lisa had lost 12%\text{12}\% of her original weight. She lost 2121 pounds. What was Lisa's original weight?

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9.1 Exercise 44

Use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Tim left a $9\$\text{9} tip for a $50\$\text{50} restaurant bill. What percent tip did he leave?

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9.1 Exercise 46

Use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Yuki bought a dress on sale for $72.\$\text{72} . The sale price was 60%\text{60}\% of the original price. What was the original price of the dress?

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9.1 Exercise 48

Solve each number word problem.

The sum of a number and eight is 12.12 . Find the number.

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9.1 Exercise 50

Solve each number word problem.

The difference of a number and twelve is 3.3 . Find the number.

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9.1 Exercise 52

Solve each number word problem.

The sum of three times a number and eight is 23.23 . Find the number.

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9.1 Exercise 54

Solve each number word problem.

The difference of twice a number and seven is 17.17 . Find the number.

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9.1 Exercise 56

Solve each number word problem.

Three times the sum of a number and nine is 12.12 . Find the number.

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9.1 Exercise 58

Solve each number word problem.

One number is six more than the other. Their sum is forty-two. Find the numbers.

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9.1 Exercise 60

Solve each number word problem.

The sum of two numbers is twenty. One number is four less than the other. Find the numbers.

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9.1 Exercise 62

Solve each number word problem.

A number is one more than twice another number. Their sum is negative five. Find the numbers.

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9.1 Exercise 64

Solve each number word problem.

The sum of two numbers is fourteen. One number is two less than three times the other. Find the numbers.

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9.1 Exercise 66

Solve each number word problem.

One number is fourteen less than another. If their sum is increased by seven, the result is 85.85 . Find the numbers.

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9.1 Exercise 68

Solve each number word problem.

The sum of two consecutive integers is 77.77 . Find the integers.

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9.1 Exercise 70

Solve each number word problem.

The sum of two consecutive integers is −23.−23 . Find the integers.

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9.1 Exercise 72

Solve each number word problem.

The sum of three consecutive integers is 78.78 . Find the integers.

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9.1 Exercise 74

Solve each number word problem.

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

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9.1 Exercise 76

Shopping Patty paid $35\$\text{35} for a purse on sale for $10\$\text{10} off the original price. What was the original price of the purse?

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9.1 Exercise 78

Shopping Minh spent $6.25\$\text{6}.\text{25} on 55 sticker books to give his nephews. Find the cost of each sticker book.

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9.1 Exercise 80

Shopping Tom paid $1,166.40\$\text{1},\text{166}.\text{40} for a new refrigerator, including $86.40\$\text{86}.\text{40} tax. What was the price of the refrigerator before tax?

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9.1 Exercise 82

Write a few sentences about your thoughts and opinions of word problems. Are these thoughts positive, negative, or neutral? If they are negative, how might you change your way of thinking in order to do better?

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Adapted from Prealgebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Prealgebra 2e. Imported at revision 77a933c.