Contents
- Preface
1Foundations
2Solving Linear Equations and Inequalities
- Introduction
- 2.1Solve Equations Using the Subtraction and Addition Properties of Equality
- 2.2Solve Equations using the Division and Multiplication Properties of Equality
- 2.3Solve Equations with Variables and Constants on Both Sides
- 2.4Use a General Strategy to Solve Linear Equations
- 2.5Solve Equations with Fractions or Decimals
- Index
Review Exercises
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.
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?
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.
Twice the difference of a number and ten is fifty-four. Find the number.
One number is eleven more than another. If their sum is increased by seventeen, the result is 90. Find the numbers.
The sum of two consecutive integers is Find the numbers.
Find three consecutive even integers whose sum is 234.
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.
300% of 82 is what number?
72 is 30% of what number?
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?
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?
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.
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?
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?
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.
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.
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.
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.
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?
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?
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?
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?
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?
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?
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?
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.
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?
What is the height of a triangle with area 67.5 square meters and base 9 meters?
One angle of a triangle is more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.
One angle of a right triangle measures What is the measure of the other angles of the triangle?
The measure of the smallest angle in a right triangle is less than the measure of the next larger angle. Find the measures of all three angles.
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.
In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.
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?
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.
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 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.
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.
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?
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.
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?
Rogelio paints watercolors. He got a $100 gift card to the art supply store and wants to use it to buy 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?
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?
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?