# Exercises: Use a Problem-Solving Strategy and Applications (3.7)

## Exercises: Use the Approach Word Problems with a Positive Attitude

Instructions: For questions 1-2, prepare the lists described.

1. 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.
Solution

2. List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.

## Exercises: Use a Problem-Solving Strategy for Word Problems

Instructions: For questions 3-14, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

3. 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?
Solution

$30$ children

4. Three-fifths of the members of the school choir are women. If there are 24 women, what is the total number of choir members?

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

$125$ CDs

6. One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag?

7. 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.
Solution

$6$ boys

8. There are 18 Cub Scouts in Pack 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.

9. 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?
Solution

$58$ books

10. Jeff is lining up children’s and adult bicycles at the bike shop where he works. The number of children’s bicycles is nine less than three times the number of adult bicycles. There are 42 adult bicycles. How many children’s bicycles are there?

11. 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?
Solution

$750$

12. Marc just bought an SUV for $54,000$. This is $7,400$ less than twice what his wife paid for her car last year. How much did his wife pay for her car?

13. 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?
Solution

$13,500$

14. Erica earned a total of $50,450$ last year from her two jobs. The amount she earned from her job at the store was $1,250$ more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?

## Exercises: Solve Number Problems

Instructions: For questions 15-56, solve each number word problem.

15. The sum of a number and eight is $12$. Find the number.
Solution

$4$

16. The sum of a number and nine is $17$. Find the number.

17. The difference of a number and $12$ is three. Find the number.
Solution

$15$

18. The difference of a number and eight is four. Find the number.

19. The sum of three times a number and eight is $23$. Find the number.
Solution

$5$

20. The sum of twice a number and six is $14$. Find the number.

21. The difference of twice a number and seven is $17$. Find the number.
Solution

$12$

22. The difference of four times a number and seven is $21$. Find the number.

23. Three times the sum of a number and nine is $12$. Find the number.
Solution

$-5$

24. Six times the sum of a number and eight is $30$. Find the number.

25. One number is six more than the other. Their sum is $42$. Find the numbers.
Solution

18, 24

26. One number is five more than the other. Their sum is $33$. Find the numbers.

27. The sum of two numbers is $20$. One number is four less than the other. Find the numbers.
Solution

$8,12$

28. The sum of two numbers is $27$. One number is seven less than the other. Find the numbers.

29. The sum of two numbers is $-45$. One number is nine more than the other. Find the numbers.
Solution

$-18,-27$

30. The sum of two numbers is $-61$. One number is $35$ more than the other. Find the numbers.

31. The sum of two numbers is $-316$. One number is $94$ less than the other. Find the numbers.
Solution

$-111,-205$

32. The sum of two numbers is $-284$. One number is $62$ less than the other. Find the numbers.

33. One number is $14$ less than another. If their sum is increased by seven, the result is $85$. Find the numbers.
Solution

$32,46$

34. One number is $11$ less than another. If their sum is increased by eight, the result is $71$. Find the numbers.

35. One number is five more than another. If their sum is increased by nine, the result is $60$. Find the numbers.
Solution

$23,28$

36. One number is eight more than another. If their sum is increased by $17$, the result is $95$. Find the numbers.

37. One number is one more than twice another. Their sum is $-5$. Find the numbers.
Solution

$-2,-3$

38. One number is six more than five times another. Their sum is six. Find the numbers.

39. The sum of two numbers is $14$. One number is two less than three times the other. Find the numbers.
Solution

$4,10$

40. The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.

41. The sum of two consecutive integers is $77$. Find the integers.
Solution

$38,39$

42. The sum of two consecutive integers is $89$. Find the integers.

43. The sum of two consecutive integers is $-23$. Find the integers.
Solution

$-11,-12$

44. The sum of two consecutive integers is $-37$. Find the integers.

45. The sum of three consecutive integers is $78$. Find the integers.
Solution

$25,26,27$

46. The sum of three consecutive integers is $60$. Find the integers.

47. Find three consecutive integers whose sum is $-36$.
Solution

$-11,-12,-13$

48. Find three consecutive integers whose sum is $-3$.

49. Find three consecutive even integers whose sum is $258$.
Solution

$84,86,88$

50. Find three consecutive even integers whose sum is $222$.

51. Find three consecutive odd integers whose sum is $171$.
Solution

$55,57,59$

52. Find three consecutive odd integers whose sum is $291$.

53. Find three consecutive even integers whose sum is $-36$.
Solution

$-10,-12,-14$

54. Find three consecutive even integers whose sum is $-84$.

55. Find three consecutive odd integers whose sum is $-213$.
Solution

$-69,-71,-73$

56. Find three consecutive odd integers whose sum is $-267$.

## Exercises: Translate and Solve Basic Percent Equations

Instructions: For questions 57-80, translate and solve.

57. What number is $45\%$ of $120$?
Solution

$54$

58. What number is $65\%$ of $100$?

59. What number is $24\%$ of $112$?
Solution

$26.88$

60. What number is $36\%$ of $124$?

61. $250\%$ of $65$ is what number?
Solution

$162.5$

62. $150\%$ of $90$ is what number?

63. $800\%$ of $2250$ is what number?
Solution

$18\text{,}000$

64. $600\%$ of $1740$ is what number?

65. $28$ is $25\%$ of what number?
Solution

$112$

66. $36$ is $25\%$ of what number?

67. $81$ is $75\%$ of what number?
Solution

$108$

68. $93$ is $75\%$ of what number?

69. $8.2\%$ of what number is $2.87$?
Solution

$35$

70. $6.4\%$ of what number is $2.88$?

71. $11.5\%$ of what number is $108.10$?
Solution

$940$

72. $12.3\%$ of what number is $92.25$?

73. What percent of $260$ is $78$?
Solution

$30\%$

74. What percent of $215$ is $86$?

75. What percent of $1500$ is $540$?
Solution

$36\%$

76. What percent of $1800$ is $846$?

77. $30$ is what percent of $20$?
Solution

$150\%$

78. $50$ is what percent of $40$?

79. $840$ is what percent of $480$?
Solution

$175\%$

80. $790$ is what percent of $395$?

## Exercises: Solve Percent Applications

Instructions: For questions 81-98, solve.

81. Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25$. Geneva wants to leave $16\%$ of the total bill as a tip. How much should the tip be?
Solution

$11.88$

82. When Hiro and his co-workers had lunch at a restaurant near their work, the bill was $90.50$. They want to leave $18\%$ of the total bill as a tip. How much should the tip be?

83. Trong has $12\%$ of each paycheck automatically deposited to his savings account. His last paycheck was $2165$. How much money was deposited to Trong’s savings account?
Solution

$259.80$

84. Cherise deposits $8\%$ of each paycheck into her retirement account. Her last paycheck was $1,485$. How much did Cherise deposit into her retirement account?

85. One serving of oatmeal has eight grams of fiber, which is $33\%$ of the recommended daily amount. What is the total recommended daily amount of fiber?
Solution

$24.2$ g

86. One serving of trail mix has $67$ grams of carbohydrates, which is $22\%$ of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

87. A bacon cheeseburger at a popular fast food restaurant contains $2070$ milligrams (mg) of sodium, which is $86\%$ of the recommended daily amount. What is the total recommended daily amount of sodium?
Solution

$2407$ mg

88. A grilled chicken salad at a popular fast food restaurant contains $650$ milligrams (mg) of sodium, which is $27\%$ of the recommended daily amount. What is the total recommended daily amount of sodium?

89. After 3 months on a diet, Lisa had lost $12\%$ of her original weight. She lost $21$ pounds. What was Lisa’s original weight?
Solution

$175$ lb.

90. Tricia got a $6\%$ raise on her weekly salary. The raise was $30$ per week. What was her original salary?

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

$120$

92. Kim bought a pair of shoes on sale for $40.50$. The sale price was $45\%$ of the original price. What was the original price of the shoes?

93. Tim left a $9$ tip for a $50$ restaurant bill. What percent tip did he leave?
Solution

$18\%$

94. Rashid left a $15$ tip for a $75$ restaurant bill. What percent tip did he leave?

95. The nutrition fact sheet at a fast food restaurant says the fish sandwich has $380$ calories, and $171$ calories are from fat. What percent of the total calories is from fat?
Solution

$45\%$

96. The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has $190$ calories, and $114$ calories are from fat. What percent of the total calories is from fat?

97. Emma gets paid $3\text{,}000$ per month. She pays $750$ a month for rent. What percent of her monthly pay goes to rent?
Solution

$25\%$

98. Dimple gets paid $3\text{,}200$ per month. She pays $960$ a month for rent. What percent of her monthly pay goes to rent?

## Exercises: Find Percent Increase and Percent Decrease

Instructions: For questions 99-110, solve.

99. Tamanika got a raise in her hourly pay, from $15.50$ to $17.36$. Find the percent increase.
Solution

$12\%$

100. Ayodele got a raise in her hourly pay, from $24.50$ to $25.48$. Find the percent increase.

101. Annual student fees at the University of California rose from about $4\text{,}000$ in 2000 to about $12\text{,}000$ in 2010. Find the percent increase.
Solution

$200\%$

102. The price of a share of one stock rose from $12.50$ to $50$. Find the percent increase.

103. According to Time magazine annual global seafood consumption rose from $22$ pounds per person in the 1960s to $38$ pounds per person in 2011. Find the percent increase. (Round to the nearest tenth of a percent.)
Solution

$72.7\%$

104. In one month, the median home price in the Northeast rose from $225\text{,}400$ to $241\text{,}500$. Find the percent increase. (Round to the nearest tenth of a percent.)

105. A grocery store reduced the price of a loaf of bread from $2.80$ to $2.73$. Find the percent decrease.
Solution

$2.5\%$

106. The price of a share of one stock fell from $8.75$ to $8.54$. Find the percent decrease.

107. Hernando’s salary was $49,500$ last year. This year his salary was cut to $44,055$. Find the percent decrease.
Solution

$11\%$

108. In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the percent decrease.

109. In 1 month, the median home price in the West fell from $203\text{,}400$ to $192\text{,}300$. Find the percent decrease. (Round to the nearest tenth of a percent.)
Solution

$5.5\%$

110. Sales of video games and consoles fell from $1\text{,}150$ million to $1\text{,}030$ million in 1 year. Find the percent decrease. (Round to the nearest tenth of a percent.)

## Exercises: Solve Simple Interest Applications

Instructions: For questions 111-122, solve.

111. Casey deposited $1\text{,}450$ in a bank account with interest rate $4\%$. How much interest was earned in two years?
Solution

$116$

112. Terrence deposited $5\text{,}720$ in a bank account with interest rate $6\%$. How much interest was earned in 4 years?

113. Robin deposited $31\text{,}000$ in a bank account with interest rate $5.2\%$. How much interest was earned in 3 years?
Solution

$4,836$

114. Carleen deposited $16\text{,}400$ in a bank account with interest rate $3.9\%$. How much interest was earned in 8 years?

115. Hilaria borrowed $8\text{,}000$ from her grandfather to pay for college. Five years later, she paid him back the $8\text{,}000$, plus $1\text{,}200$ interest. What was the rate of interest?
Solution

$3\%$

116. Kenneth loaned his niece $1\text{,}200$ to buy a computer. Two years later, she paid him back the $1\text{,}200$, plus $96$ interest. What was the rate of interest?

117. Lebron loaned his daughter $20\text{,}000$ to help her buy a condominium. When she sold the condominium four years later, she paid him the $20\text{,}000$, plus $3\text{,}000$ interest. What was the rate of interest?
Solution

$3.75\%$

118. Pablo borrowed $50\text{,}000$ to start a business. Three years later, he repaid the $50\text{,}000$, plus $9\text{,}375$ interest. What was the rate of interest?

119. In 10 years, a bank account that paid $5.25\%$ earned $18\text{,}375$ interest. What was the principal of the account?
Solution

$35\text{,}000$

120. In 25 years, a bond that paid $4.75\%$ earned $2\text{,}375$ interest. What was the principal of the bond?

121. Joshua’s computer loan statement said he would pay $1\text{,}244.34$in interest for a 3-year loan at $12.4\%$. How much did Joshua borrow to buy the computer?
Solution

$3\text{,}345$

122. Margaret’s car loan statement said she would pay $7\text{,}683.20$ in interest for a 5-year loan at $9.8\%$. How much did Margaret borrow to buy the car?

## Exercises: Solve Applications with Discount or Mark-up

Instructions: For questions 123-126, find the sale price.

123. Perla bought a cell phone that was on sale for $50$ off. The original price of the cell phone was $189$.
Solution

$139$

124. Sophie saw a dress she liked on sale for $15$ off. The original price of the dress was $96$.

125. Rick wants to buy a tool set with original price $165$. Next week the tool set will be on sale for $40$ off.
Solution

$125$

126. Angelo’s store is having a sale on televisions. One television, with original price $859$, is selling for $125$ off.

## Exercises: Find Discount and Sales Price Amounts

Instructions: For questions 127-132, find

a. the amount of discount
b. the sale price.

127. Janelle bought a beach chair on sale at $60\%$ off. The original price was $44.95$.
Solution

a. $26.97$
b. $17.98$

128. Errol bought a skateboard helmet on sale at $40\%$ off. The original price was $49.95$.

129. Kathy wants to buy a camera that lists for $389$. The camera is on sale with a $33\%$ discount.
Solution

a. $128.37$
b. $260.63$

130. Colleen bought a suit that was discounted $25\%$ from an original price of $245$.

131. Erys bought a treadmill on sale at $35\%$ off. The original price was $949.95$ (round to the nearest cent.)
Solution

a. $332.48$
b. $617.47$

132. Jay bought a guitar on sale at $45\%$ off. The original price was $514.75$ (round to the nearest cent.)

## Exercises: Find Discount and Discount Rate Amounts

Instructions: For questions 133-138, find

a. the amount of discount
b. the discount rate (Round to the nearest tenth of a percent if needed)

133. Larry and Donna bought a sofa at the sale price of $1\text{,}344$. The original price of the sofa was $1\text{,}920$.
Solution

a. $576$
b. $30\%$

134. Hiroshi bought a lawnmower at the sale price of $240$. The original price of the lawnmower is $300$.

135. Patty bought a baby stroller on sale for $301.75$. The original price of the stroller was $355$.
Solution

a. $53.25$
b. $15\%$

136. Bill found a book he wanted on sale for $20.80$. The original price of the book was $32$.

137. Nikki bought a patio set on sale for $480$. The original price was $850$. To the nearest tenth of a percent, what was the rate of discount?
Solution

a. $370$
b. $43.5\%$

138. Stella bought a dinette set on sale for $725$. The original price was $1\text{,}299$. To the nearest tenth of a percent, what was the rate of discount?

## Exercises: Find Mark-up and List Price Amounts

Instructions: For questions 139-144, find

a. the amount of the mark-up
b. the list price.

139. Daria bought a bracelet at original cost $16$ to sell in her handicraft store. She marked the price up $45\%$.
Solution

a. $7.20$
b. $23.20$

140. Regina bought a handmade quilt at original cost $120$ to sell in her quilt store. She marked the price up $55\%$.

141. Tom paid $0.60$ a pound for tomatoes to sell at his produce store. He added a $33\%$ mark-up.
Solution

a. $0.20$
b. $0.80$

142. Flora paid her supplier $0.74$ a stem for roses to sell at her flower shop. She added an $85\%$ mark-up.

143. Alan bought a used bicycle for $115$. After re-conditioning it, he added $225\%$ mark-up and then advertised it for sale.
Solution

a. $258.75$
b. $373.75$

144. Michael bought a classic car for $8\text{,}500$. He restored it, then added $150\%$ mark-up before advertising it for sale.

## Exercises: Everyday Math

Instructions: For questions 149-152, answer the given everyday math word problems.
145. Sale Price. Patty paid $35$ for a purse on sale for $10$ off the original price. What was the original price of the purse?
Solution

$45$

146. Sale Price. Travis bought a pair of boots on sale for $25$ off the original price. He paid $60$ for the boots. What was the original price of the boots?

147. Buying in Bulk. Minh spent $6.25$ on five sticker books to give his nephews. Find the cost of each sticker book.
Solution

$1.25$

148. Buying in Bulk. Alicia bought a package of eight peaches for $3.20$. Find the cost of each peach.

149. Price before Sales Tax. Tom paid $1\text{,}166.40$ for a new refrigerator, including $86.40$ tax. What was the price of the refrigerator?
Solution

$1080$

150. Price before Sales Tax. Kenji paid $2\text{,}279$ for a new living room set, including $129$ tax. What was the price of the living room set?

151. Leaving a Tip. At the campus coffee cart, a medium coffee costs $1.65$. MaryAnne brings $2.00$ with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?

Solution

$21.2\%$

152. Splitting a Bill. Four friends went out to lunch and the bill came to $53.75$. They decided to add enough tip to make a total of $64$, so that they could easily split the bill evenly among themselves. What percent tip did they leave?

## Exercises: Writing Exercises

Instructions: For questions 153-160, answer the given writing exercises.
153. What has been your past experience solving word problems?
Solution

154. When you start to solve a word problem, how do you decide what to let the variable represent?

155. What are consecutive odd integers? Name three consecutive odd integers between 50 and 60.
Solution

Consecutive odd integers are odd numbers that immediately follow each other. An example of three consecutive odd integers between 50 and 60 would be 51, 53, and 55.

156. What are consecutive even integers? Name three consecutive even integers between $-50$ and $-40$.

157. Without solving the problem “$44$ is $80\%$ of what number” think about what the solution might be. Should it be a number that is greater than $44$ or less than $44$? Explain your reasoning.
Solution

The number should be greater than $44$. Since $80\%$ equals $0.8$ in decimal form, $0.8$ is less than one, and we must multiply the number by $0.8$ to get $44$, the number must be greater than $44$.

158. Without solving the problem “What is $20\%$ of $300$?” think about what the solution might be. Should it be a number that is greater than $300$ or less than $300$? Explain your reasoning.

159. After returning from vacation, Alex said he should have packed $50\%$ fewer shorts and $200\%$ more shirts. Explain what Alex meant.
Solution

He meant that he should have packed half the shorts and twice the shirts.

160. Because of road construction in one city, commuters were advised to plan that their Monday morning commute would take $150\%$ of their usual commuting time. Explain what this means.