Section 2.3E: Exercises
- Page ID
- 33033
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\ket}[1]{\left| #1 \right>}\)
\(\newcommand{\bra}[1]{\left< #1 \right|}\)
\(\newcommand{\braket}[2]{\left< #1 \vphantom{#2} \right| \left. #2 \vphantom{#1} \right>}\)
\(\newcommand{\braopket}[3]{\left< #1 \vphantom{#2}\vphantom{#3} \right| #2 \vphantom{#1}\vphantom{#3} \left| #3 \vphantom{#1}\vphantom{#2} \right>}\)
\(\newcommand{\qmvec}[1]{\mathbf{\vec{#1}}}\)
\(\newcommand{\op}[1]{\hat{\mathbf{#1}}}\)
\(\newcommand{\expect}[1]{\langle #1 \rangle}\)
\(\newcommand{\dfn}[1]{\emph{\textbf{#1}}}\)
Practice Makes Perfect
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.
- Answer
-
Answers will vary.
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.
In the following exercises, 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.
- Answer
-
six boys
There are 18 Cub Scouts in Troop 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.
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?
- Answer
-
58 hardback books
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?
Solve Number Word Problems
In the following exercises, solve each number word problem.
The difference of a number and 12 is three. Find the number.
- Answer
-
\(15\)
The difference of a number and eight is four. Find the number.
The sum of three times a number and eight is 23. Find the number.
- Answer
-
\(5\)
The sum of twice a number and six is 14. Find the number.
The difference of twice a number and seven is 17. Find the number.
- Answer
-
\(12\)
The difference of four times a number and seven is 21. Find the number.
Three times the sum of a number and nine is 12. Find the number.
- Answer
-
\(-5\)
Six times the sum of a number and eight is \(30\). Find the number.
One number is six more than the other. Their sum is \(42\). Find the numbers.
- Answer
-
\(18, 24\)
One number is five more than the other. Their sum is \(33\). Find the numbers.
The sum of two numbers is 20. One number is four less than the other. Find the numbers.
- Answer
-
\(8, 12\)
The sum of two numbers is 27. One number is seven less than the other. Find the numbers.
One number is 14 less than another. If their sum is increased by seven, the result is 85. Find the numbers.
- Answer
-
\(32, 46\)
One number is 11 less than another. If their sum is increased by eight, the result is 71. Find the numbers.
The sum of two numbers is 14. One number is two less than three times the other. Find the numbers.
- Answer
-
\(4, 10\)
The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.
The sum of two consecutive integers is 77. Find the integers.
- Answer
-
\(38, 39\)
The sum of two consecutive integers is 89. Find the integers.
The sum of three consecutive integers is 78. Find the integers.
- Answer
-
\(25, 26, 27\)
The sum of three consecutive integers is 60. Find the integers.
Find three consecutive integers whose sum is \(−36\).
- Answer
-
\(−11,−12,−13\)
Find three consecutive integers whose sum is \(−3\).
Find three consecutive even integers whose sum is 258.
- Answer
-
\(84, 86, 88\)
Find three consecutive even integers whose sum is 222.
Find three consecutive odd integers whose sum is \(−213\).
- Answer
-
\(−69,−71,−73\)
Find three consecutive odd integers whose sum is \(−267\).
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?
- Answer
-
$750
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?
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?
- Answer
-
$13,500
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?
Solve Percent Applications
In the following exercises, translate and solve.
ⓐ What number is 45% of 120? ⓑ 81 is 75% of what number? ⓐ What percent of 260 is 78?
- Answer
-
ⓐ 54 ⓑ 108 ⓐ 30%
ⓐ What number is 65% of 100? ⓑ 93 is 75% of what number? ⓐ What percent of 215 is 86?
ⓐ 250% of 65 is what number? ⓑ 8.2% of what amount is $2.87? ⓐ 30 is what percent of 20?
- Answer
-
ⓐ162.5 ⓑ $35 ⓐ 150%
ⓐ 150% of 90 is what number? ⓑ 6.4% of what amount is $2.88? ⓐ 50 is what percent of 40?
In the following exercises, solve.
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?
- Answer
-
$11.88
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?
One serving of oatmeal has 8 grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber?
- Answer
-
24.2 g
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?
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?
- Answer
-
2407 mg
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?
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?
- Answer
-
45%
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?
Emma gets paid $3,000 per month. She pays $750 a month for rent. What percent of her monthly pay goes to rent?
- Answer
-
25%
Dimple gets paid $3,200 per month. She pays $960 a month for rent. What percent of her monthly pay goes to rent?
In the following exercises, solve.
Tamanika received a raise in her hourly pay, from $15.50 to $17.36. Find the percent change.
- Answer
-
12%
Ayodele received a raise in her hourly pay, from $24.50 to $25.48. Find the percent change.
Annual student fees at the University of California rose from about $4,000 in 2000 to about $12,000 in 2010. Find the percent change.
- Answer
-
200%
The price of a share of one stock rose from $12.50 to $50. Find the percent change.
A grocery store reduced the price of a loaf of bread from $2.80 to $2.73. Find the percent change.
- Answer
-
−2.5%
The price of a share of one stock fell from $8.75 to $8.54. Find the percent change.
Hernando’s salary was $49,500 last year. This year his salary was cut to $44,055. Find the percent change.
- Answer
-
−11%
In ten years, the population of Detroit fell from 950,000 to about 712,500. Find the percent change.
In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.
Janelle bought a beach chair on sale at 60% off. The original price was $44.95.
- Answer
-
ⓐ $26.97 ⓑ $17.98
Errol bought a skateboard helmet on sale at 40% off. The original price was $49.95.
In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate (Round to the nearest tenth of a percent if needed.)
Larry and Donna bought a sofa at the sale price of $1,344. The original price of the sofa was $1,920.
- Answer
-
ⓐ $576 ⓑ 30%
Hiroshi bought a lawnmower at the sale price of $240. The original price of the lawnmower is $300.
In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.
Daria bought a bracelet at original cost $16 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet?
- Answer
-
ⓐ $7.20 ⓑ $23.20
Regina bought a handmade quilt at original cost $120 to sell in her quilt store. She marked the price up 55%. What was the list price of the quilt?
Tom paid $0.60 a pound for tomatoes to sell at his produce store. He added a 33% mark-up. What price did he charge his customers for the tomatoes?
- Answer
-
ⓐ $0.20 ⓑ $0.80
Flora paid her supplier $0.74 a stem for roses to sell at her flower shop. She added an 85% mark-up. What price did she charge her customers for the roses?
Solve Simple Interest Applications
In the following exercises, solve.
Casey deposited $1,450 in a bank account that earned simple interest at an interest rate of 4%. How much interest was earned in two years?
- Answer
-
$116
Terrence deposited $5,720 in a bank account that earned simple interest at an interest rate of 6%. How much interest was earned in four years?
Robin deposited $31,000 in a bank account that earned simple interest at an interest rate of 5.2%. How much interest was earned in three years?
- Answer
-
$4836
Carleen deposited $16,400 in a bank account that earned simple interest at an interest rate of 3.9% How much interest was earned in eight years?
Hilaria borrowed $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000, plus $1,200 interest. What was the rate of simple interest?
- Answer
-
3%
Kenneth lent his niece $1,200 to buy a computer. Two years later, she paid him back the $1,200, plus $96 interest. What was the rate of simple interest?
Lebron lent his daughter $20,000 to help her buy a condominium. When she sold the condominium four years later, she paid him the $20,000, plus $3,000 interest. What was the rate of simple interest?
- Answer
-
3.75%
Pablo borrowed $50,000 to start a business. Three years later, he repaid the $50,000, plus $9,375 interest. What was the rate of simple interest?
In 10 years, a bank account that paid 5.25% simple interest earned $18,375 interest. What was the principal of the account?
- Answer
-
$35,000
In 25 years, a bond that paid 4.75% simple interest earned $2,375 interest. What was the principal of the bond?
Joshua’s computer loan statement said he would pay $1,244.34 in simple interest for a three-year loan at 12.4%. How much did Joshua borrow to buy the computer?
- Answer
-
$3345
Margaret’s car loan statement said she would pay $7,683.20 in simple interest for a five-year loan at 9.8%. How much did Margaret borrow to buy the car?
Everyday Math
Tipping 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?
- Answer
-
17.5%
Tipping 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?
Writing Exercises
What has been your past experience solving word problems? Where do you see yourself moving forward?
- Answer
-
Answers will vary.
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.
After returning from vacation, Alex said he should have packed 50% fewer shorts and 200% more shirts. Explain what Alex meant.
- Answer
-
Answers will vary.
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.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objective of this section.
ⓑ After reviewing this checklist, what will you do to become confident for all objectives?