Chapter 3 Review Exercises
- Page ID
- 30501
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chapter 3 Review Exercises
3.1 Using a Problem Solving Strategy
Approach Word Problems with a Positive Attitude
In the following exercises, reflect on your approach to word problems.
How has your attitude towards solving word problems changed as a result of working through this chapter? Explain.
- Answer
-
answers will vary
Did the problem-solving strategy help you solve word problems in this chapter? Explain.
Use a Problem-Solving Strategy for Word Problems
In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question.
Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?
- Answer
-
116
There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.
Solve Number Problems
In the following exercises, solve each number word problem.
The sum of a number and three is forty-one. Find the number.
- Answer
-
38
Twice the difference of a number and ten is fifty-four. Find the number.
One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.
- Answer
-
−18,−9
One number is eleven more than another. If their sum is increased by seventeen, the result is 90. Find the numbers.
One number is two more than four times another. Their sum is −13. Find the numbers.
- Answer
-
−3,−10
The sum of two consecutive integers is −135. Find the numbers.
Find three consecutive integers whose sum is −141.
- Answer
-
−48,−47,−46
Find three consecutive even integers whose sum is 234.
Find three consecutive odd integers whose sum is 51.
- Answer
-
15, 17, 19
Koji has $5,502 in his savings account. This is $30 less than six times the amount in his checking account. How much money does Koji have in his checking account?
3.2 Solve Percent Applications
Translate and Solve Basic Percent Equations
In the following exercises, translate and solve.
What number is 67% of 250?
- Answer
-
167.5
300% of 82 is what number?
12.5% of what number is 20?
- Answer
-
160
72 is 30% of what number?
What percent of 125 is 150?
- Answer
-
120%
127.5 is what percent of 850?
Solve Percent Applications
In the following exercises, solve.
The bill for Dino’s lunch was $19.45. He wanted to leave 20% of the total bill as a tip. How much should the tip be?
- Answer
-
$3.89
Reza was very sick and lost 15% of his original weight. He lost 27 pounds. What was his original weight?
Dolores bought a crib on sale for $350. The sale price was 40% of the original price. What was the original price of the crib?
- Answer
-
$875
Jaden earns $2,680 per month. He pays $938 a month for rent. What percent of his monthly pay goes to rent?
Find Percent Increase and Percent Decrease
In the following exercises, solve.
Angel’s got a raise in his annual salary from $55,400 to $56,785. Find the percent increase.
- Answer
-
2.5%
Rowena’s monthly gasoline bill dropped from $83.75 last month to $56.95 this month. Find the percent decrease.
Solve Simple Interest Applications
In the following exercises, solve.
Winston deposited $3,294 in a bank account with interest rate 2.6%. How much interest was earned in 5 years?
- Answer
-
$428.22
Moira borrowed $4,500 from her grandfather to pay for her first year of college. Three years later, she repaid the $4,500 plus $243 interest. What was the rate of interest?
Jaime’s refrigerator loan statement said he would pay $1,026 in interest for a 4-year loan at 13.5%. How much did Jaime borrow to buy the refrigerator?
- Answer
-
$1,900
In 12 years, a bond that paid 6.35% interest earned $7,620 interest. What was the principal of the bond?
Solve Applications with Discount or Mark-up
In the following exercises, find the sale price.
The original price of a handbag was $84. Carole bought it on sale for $21 off.
- Answer
-
$63
Marian wants to buy a coffee table that costs $495. Next week the coffee table will be on sale for $149 off.
In the following exercises, find
- the amount of discount and
- the sale price.
Emmett bought a pair of shoes on sale at 40% off from an original price of $138.
- Answer
-
- $55.20
- $82.80
Anastasia bought a dress on sale at 75% off from an original price of $280.
In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent, if needed.)
Zack bought a printer for his office that was on sale for $380. The original price of the printer was $450.
- Answer
-
- $70
- 15.6%
Lacey bought a pair of boots on sale for $95. The original price of the boots was $200.
In the following exercises, find
- the amount of the mark-up and
- the list price.
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350% mark-up.
- Answer
-
- $175
- $225
Carly bought bottled water for $0.24 per bottle at the discount store. She added a 75% mark-up before selling them at the football game.
3.3 Solve Mixture Applications
Solve Coin Word Problems
In the following exercises, solve each coin word problem.
Francie has $4.35 in dimes and quarters. The number of dimes is five more than the number of quarters. How many of each coin does she have?
- Answer
-
16 dimes, 11 quarters
Scott has $0.39 in pennies and nickels. The number of pennies is eight times the number of nickels. How many of each coin does he have?
Paulette has $140 in $5 and $10 bills. The number of $10 bills is one less than twice the number of $5 bills. How many of each does she have?
- Answer
-
six $5 bills, 11 $10 bills
Lenny has $3.69 in pennies, dimes, and quarters. The number of pennies is three more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he have?
Solve Ticket and Stamp Word Problems
In the following exercises, solve each ticket or stamp word problem.
A church luncheon made $842. Adult tickets cost $10 each and children’s tickets cost $6 each. The number of children was 12 more than twice the number of adults. How many of each ticket were sold?
- Answer
-
35 adults, 82 children
Tickets for a basketball game cost $2 for students and $5 for adults. The number of students was three less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold?
125 tickets were sold for the jazz band concert for a total of $1,022. Student tickets cost $6 each and general admission tickets cost $10 each. How many of each kind of ticket were sold?
- Answer
-
57 students, 68 adults
One afternoon the water park sold 525 tickets for a total of $13,545. Child tickets cost $19 each and adult tickets cost $40 each. How many of each kind of ticket were sold?
Ana spent $4.06 buying stamps. The number of $0.41 stamps she bought was five more than the number of $0.26 stamps. How many of each did she buy?
- Answer
-
three $0.26 stamps, eight $0.41 stamps
Yumi spent $34.15 buying stamps. The number of $0.56 stamps she bought was 10 less than four times the number of $0.41 stamps. How many of each did she buy?
Solve Mixture Word Problems
In the following exercises, solve each mixture word problem.
Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost $3.45 per pound and nuts cost $7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him $6.96 per pound?
- Answer
-
2.2 lb. of raisins, 7.8 lb. of nuts
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tile. She will use basic tiles that cost $8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?
Shawn has $15,000 to invest. She will put some of it into a fund that pays 4.5% annual interest and the rest in a certificate of deposit that pays 1.8% annual interest. How much should she invest in each account if she wants to earn 4.05% annual interest on the total amount?
- Answer
-
$12,500 at 4.5%, $2,500 at 1.8%
Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? (Round your answer to the nearest tenth of a percent.)
3.4 Solve Geometry Applications: Triangles, Rectangles and the Pythagorean Theorem
Solve Applications Using Triangle Properties
In the following exercises, solve using triangle properties.
The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle.
- Answer
-
73°
The playground at a shopping mall is a triangle with perimeter 48 feet. The lengths of two sides are 19 feet and 14 feet. How long is the third side?
A triangular road sign has base 30 inches and height 40 inches. What is its area?
- Answer
-
600 square inches
What is the height of a triangle with area 67.5 square meters and base 9 meters?
One angle of a triangle is 30° more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.
- Answer
-
30°,60°,90°
One angle of a right triangle measures 58°. What is the measure of the other angles of the triangle?
The measure of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. Find the measures of all three angles.
- Answer
-
22.5°,67.5°,90°
The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more than the smallest side. The third side is six feet more than twice the smallest side. Find the lengths of all sides.
Use the Pythagorean Theorem
In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.
- Answer
-
26
In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.
- Answer
-
8
- Answer
-
8.1
In the following exercises, solve. Approximate to the nearest tenth, if necessary.
Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is 8 feet tall and Sergio has 10 feet of wire. How far from the base of the antenna can he attach the wire?
- Answer
-
\(6^{\prime}\)
Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?
Solve Applications Using Rectangle Properties
In the following exercises, solve using rectangle properties.
The length of a rectangle is 36 feet and the width is 19 feet. Find the
- perimeter
- area.
- Answer
-
- 110 ft.
- 684 sq. ft.
A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long. Find the
- perimeter
- area.
The area of a rectangle is 2356 square meters. The length is 38 meters. What is the width?
- Answer
-
62 m
The width of a rectangle is 45 centimeters. The area is 2,700 square centimeters. What is the length?
The length of a rectangle is 12 cm more than the width. The perimeter is 74 cm. Find the length and the width.
- Answer
-
24.5 cm, 12.5 cm
The width of a rectangle is three more than twice the length. The perimeter is 96 inches. Find the length and the width.
3.5 Solve Uniform Motion Applications
Solve Uniform Motion Applications
In the following exercises, solve.
When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa 2 hours to drive the same distance. Elsa’s speed is seven miles per hour faster than Gabe’s speed. Find Gabe’s speed and Elsa’s speed.
- Answer
-
Gabe 70 mph, Elsa 77 mph
Louellen and Tracy met at a restaurant on the road between Chicago and Nashville. Louellen had left Chicago and drove 3.2 hours towards Nashville. Tracy had left Nashville and drove 4 hours towards Chicago, at a speed one mile per hour faster than Louellen’s speed. The distance between Chicago and Nashville is 472 miles. Find Louellen’s speed and Tracy’s speed.
Two busses leave Amarillo at the same time. The Albuquerque bus heads west on the I-40 at a speed of 72 miles per hour, and the Oklahoma City bus heads east on the I-40 at a speed of 78 miles per hour. How many hours will it take them to be 375 miles apart?
- Answer
-
2.5 hours
Kyle rowed his boat upstream for 50 minutes. It took him 30 minutes to row back downstream. His speed going upstream is two miles per hour slower than his speed going downstream. Find Kyle’s upstream and downstream speeds.
At 6:30, Devon left her house and rode her bike on the flat road until 7:30. Then she started riding uphill and rode until 8:00. She rode a total of 15 miles. Her speed on the flat road was three miles per hour faster than her speed going uphill. Find Devon’s speed on the flat road and riding uphill.
- Answer
-
flat road 11 mph, uphill 8 mph
Anthony drove from New York City to Baltimore, a distance of 192 miles. He left at 3:45 and had heavy traffic until 5:30. Traffic was light for the rest of the drive, and he arrived at 7:30. His speed in light traffic was four miles per hour more than twice his speed in heavy traffic. Find Anthony’s driving speed in heavy traffic and light traffic.
3.6 Solve Applications with Linear Inequalities
Solve Applications with Linear Inequalities
In the following exercises, solve.
Julianne has a weekly food budget of $231 for her family. If she plans to budget the same amount for each of the seven days of the week, what is the maximum amount she can spend on food each day?
- Answer
-
$33 per day
Rogelio paints watercolors. He got a $100 gift card to the art supply store and wants to use it to buy \(12^{\prime \prime} \times 16^{\prime \prime}\) canvases. Each canvas costs $10.99. What is the maximum number of canvases he can buy with his gift card?
Briana has been offered a sales job in another city. The offer was for $42,500 plus 8% of her total sales. In order to make it worth the move, Briana needs to have an annual salary of at least $66,500. What would her total sales need to be for her to move?
- Answer
-
at least $300,000
Renee’s car costs her $195 per month plus $0.09 per mile. How many miles can Renee drive so that her monthly car expenses are no more than $250?
Costa is an accountant. During tax season, he charges $125 to do a simple tax return. His expenses for buying software, renting an office, and advertising are $6,000. How many tax returns must he do if he wants to make a profit of at least $8,000?
- Answer
-
at least 112 jobs
Jenna is planning a 5-day resort vacation with three of her friends. It will cost her $279 for airfare, $300 for food and entertainment, and $65 per day for her share of the hotel. She has $550 saved towards her vacation and can earn $25 per hour as an assistant in her uncle’s photography studio. How many hours must she work in order to have enough money for her vacation?
Practice Test
Four-fifths of the people on a hike are children. If there are 12 children, what is the total number of people on the hike?
- Answer
-
15
One number is three more than twice another. Their sum is −63. Find the numbers.
The sum of two consecutive odd integers is −96. Find the numbers.
- Answer
-
−49,−47
Marla’s breakfast was 525 calories. This was 35% of her total calories for the day. How many calories did she have that day?
Humberto’s hourly pay increased from $16.25 to $17.55. Find the percent increase.
- Answer
-
8%
Melinda deposited $5,985 in a bank account with an interest rate of 1.9%. How much interest was earned in 2 years?
Dotty bought a freezer on sale for $486.50. The original price of the freezer was $695. Find
- the amount of discount and
- the discount rate.
- Answer
-
- $208.50
- 30%
Bonita has $2.95 in dimes and quarters in her pocket. If she has five more dimes than quarters, how many of each coin does she have?
At a concert, $1,600 in tickets were sold. Adult tickets were $9 each and children’s tickets were $4 each. If the number of adult tickets was 30 less than twice the number of children’s tickets, how many of each kind were sold?
- Answer
-
140 adult, 85 children
Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs $6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs $5.71 per gallon?
The measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is 14 more than the measure of the smallest angle. Find the measures of all three angles.
- Answer
-
41.5°,55.5°,83°
What is the height of a triangle with area 277.2 square inches and base 44 inches?
In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.
- Answer
-
10
A baseball diamond is really a square with sides of 90 feet. How far is it from home plate to second base, as shown?
- Answer
-
127.3 ft.
The length of a rectangle is two feet more than five times the width. The perimeter is 40 feet. Find the dimensions of the rectangle.
Two planes leave Dallas at the same time. One heads east at a speed of 428 miles per hour. The other plane heads west at a speed of 382 miles per hour. How many hours will it take them to be 2,025 miles apart?
- Answer
-
2.5 hours
Leon drove from his house in Cincinnati to his sister’s house in Cleveland, a distance of 252 miles. It took him 412412 hours. For the first half hour he had heavy traffic, and the rest of the time his speed was five miles per hour less than twice his speed in heavy traffic. What was his speed in heavy traffic?
Chloe has a budget of $800 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume?
- Answer
-
at most $44.44 per costume
Frank found a rental car deal online for $49 per week plus $0.24 per mile. How many miles could he drive if he wants the total cost for one week to be no more than $150?