Chapter 3: Math ModelsContent check — Elementary Algebra, Chapter 3: Math Models

Translate “6 less than twice x” into an algebraic expression.
If you missed this problem, review Example 1.26.

Solve: $\frac{2}{3}x=24.$
If you missed this problem, review Example 2.16.

Solve: $3x+8=14.$
If you missed this problem, review Example 2.27.

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

Two-fifths of the songs in Mariel’s playlist are country. If there are 16 country songs, what is the total number of songs in the playlist?

Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was 3 more than twice the number of notebooks. He bought 7 textbooks. How many notebooks did he buy?

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?

The difference of a number and eight is 17. Find the number.

The difference of a number and eleven is $\mathrm{-7}.$ Find the number.

The sum of four times a number and two is 14. Find the number.

The sum of three times a number and seven is 25. Find the number.

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

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

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

The sum of two numbers is $\mathrm{-18}.$ One number is 40 more than the other. Find the numbers.

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

One number is three more than three times another. Their sum is $\mathrm{-5}.$ Find the numbers.

The sum of two consecutive integers is $95.$ Find the numbers.

The sum of two consecutive integers is $\mathrm{-31}.$ Find the numbers.

Find three consecutive integers whose sum is $\mathrm{-96}.$

Find three consecutive integers whose sum is $\mathrm{-36}.$

Find three consecutive even integers whose sum is 102.

Find three consecutive even integers whose sum is $\mathrm{-24}.$

According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,500. This was $1,500 less than 6 times the cost in 1975. What was the average cost of a car in 1975?

U.S. Census data shows that the median price of new home in the United States in November 2014 was $280,900. This was $10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?

Use the Approach Word Problems with a Positive Attitude

In the following exercises, prepare the lists described.

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.

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.

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?

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.

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

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.

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.

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.

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?

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.

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?

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.

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?

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of two numbers is $\mathrm{-45}.$ One number is nine more than the other. Find the numbers.

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of two numbers is $\mathrm{-316}.$ One number is 94 less than the other. Find the numbers.

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

One number is one more than twice another. Their sum is $\mathrm{-5}.$ Find the numbers.

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of two consecutive integers is 77. Find the integers.

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of two consecutive integers is $\mathrm{-23}.$ Find the integers.

Solve Number Problems

In the following exercises, solve each number word problem.

The sum of three consecutive integers is 78. Find the integers.

Solve Number Problems

In the following exercises, solve each number word problem.

Find three consecutive integers whose sum is $\mathrm{-36}.$

Solve Number Problems

In the following exercises, solve each number word problem.

Find three consecutive even integers whose sum is 258.

Solve Number Problems

In the following exercises, solve each number word problem.

Find three consecutive odd integers whose sum is 171.

Solve Number Problems

In the following exercises, solve each number word problem.

Find three consecutive even integers whose sum is $\mathrm{-36}.$

Solve Number Problems

In the following exercises, solve each number word problem.

Find three consecutive odd integers whose sum is $\mathrm{-213}.$

Solve Number Problems

In the following exercises, solve each number word problem.

Sale Price Patty paid $35 for a purse on sale for $10 off the original price. What was the original price of the purse?

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

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

Solve Number Problems

In the following exercises, solve each number word problem.

What has been your past experience solving word problems?

Solve Number Problems

In the following exercises, solve each number word problem.

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

Convert 4.5% to a decimal.
If you missed this problem, review Example 1.106.

Convert 0.6 to a percent.
If you missed this problem, review Example 1.107.

Round 0.875 to the nearest hundredth.
If you missed this problem, review Example 1.94.

Multiply (4.5)(2.38).
If you missed this problem, review Example 1.98.

Solve $3.5=0.7n.$
If you missed this problem, review Example 2.13.

Subtract $50-37.45.$
If you missed this problem, review Example 1.26.

Translate and solve:

What number is 45% of 80?

Translate and solve:

What number is 55% of 60?

Translate and solve:

7.5% of what number is $1.95?

Translate and solve:

8.5% of what number is $3.06?

Translate and solve:

110 is what percent of 88?

Translate and solve:

126 is what percent of 72?

Cierra and her sister enjoyed a dinner in a restaurant and the bill was $81.50. If she wants to leave 18% of the total bill as her tip, how much should she leave?

Kimngoc had lunch at her favorite restaurant. She wants to leave 15% of the total bill as her tip. If her bill was $14.40, how much will she leave for the tip?

One serving of wheat square cereal has seven grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber?

One serving of rice cereal has 190 mg of sodium, which is 8% of the recommended daily amount. What is the total recommended daily amount of sodium?

Solve. Round to the nearest whole percent.

Veronica is planning to make muffins from a mix. The package says each muffin will be 230 calories and 60 calories will be from fat. What percent of the total calories is from fat?

Solve. Round to the nearest whole percent.

The mix Ricardo plans to use to make brownies says that each brownie will be 190 calories, and 76 calories are from fat. What percent of the total calories are from fat?

Find the percent increase. (Round to the nearest tenth of a percent.)

In 2011, the IRS increased the deductible mileage cost to 55.5 cents from 51 cents.

Find the percent increase.

In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was $2.25.

Find the percent decrease. (Round to the nearest tenth of a percent.)

The population of North Dakota was about 672,000 in 2010. The population is projected to be about 630,000 in 2020.

Find the percent decrease.

Last year, Sheila’s salary was $42,000. Because of furlough days, this year, her salary was $37,800.

Areli invested a principal of $950 in her bank account with interest rate 3%. How much interest did she earn in 5 years?

Susana invested a principal of $36,000 in her bank account with interest rate 6.5%. How much interest did she earn in 3 years?

Jim loaned his sister $5,000 to help her buy a house. In 3 years, she paid him the $5,000, plus $900 interest. What was the rate of interest?

Hang borrowed $7,500 from her parents to pay her tuition. In 5 years, she paid them $1,500 interest in addition to the $7,500 she borrowed. What was the rate of interest?

Sean’s new car loan statement said he would pay $4,866.25 in interest from an interest rate of 8.5% over 5 years. How much did he borrow to buy his new car?

In 5 years, Gloria’s bank account earned $2,400 interest at 5%. How much had she deposited in the account?

Find ⓐ the amount of discount and ⓑ the sale price:

Sergio bought a belt that was discounted 40% from an original price of $29.

Find ⓐ the amount of discount and ⓑ the sale price:

Oscar bought a barbecue that was discounted 65% from an original price of $395.

Find ⓐ the amount of discount and ⓑ the discount rate.

Lena bought a kitchen table at the sale price of $375.20. The original price of the table was $560.

Find ⓐ the amount of discount and ⓑ the discount rate.

Nick bought a multi-room air conditioner at a sale price of $340. The original price of the air conditioner was $400.

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

Jim’s music store bought a guitar at original cost $1,200. Jim marked the price up 50%.

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

The Auto Resale Store bought Pablo’s Toyota for $8,500. They marked the price up 35%.

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What number is 45% of 120?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What number is 24% of 112?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

250% of 65 is what number?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

800% of 2250 is what number?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

28 is 25% of what number?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

81 is 75% of what number?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

8.2% of what number is $2.87?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

11.5% of what number is $108.10?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What percent of 260 is 78?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What percent of 1500 is 540?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

30 is what percent of 20?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

840 is what percent of 480?

Solve Percent Applications

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?

Solve Percent Applications

In the following exercises, solve.

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?

Solve Percent Applications

In the following exercises, solve.

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?

Solve Percent Applications

In the following exercises, solve.

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?

Solve Percent Applications

In the following exercises, solve.

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

Solve Percent Applications

In the following exercises, solve.

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?

Solve Percent Applications

In the following exercises, solve.

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

Solve Percent Applications

In the following exercises, solve.

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?

Solve Percent Applications

In the following exercises, solve.

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

Find Percent Increase and Percent Decrease

In the following exercises, solve.

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

Find Percent Increase and Percent Decrease

In the following exercises, solve.

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

Find Percent Increase and Percent Decrease

In the following exercises, solve.

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.)

Find Percent Increase and Percent Decrease

In the following exercises, solve.

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

Find Percent Increase and Percent Decrease

In the following exercises, solve.

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

Find Percent Increase and Percent Decrease

In the following exercises, solve.

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

Solve Simple Interest Applications

In the following exercises, solve.

Casey deposited $1,450 in a bank account with interest rate 4%. How much interest was earned in two years?

Solve Simple Interest Applications

In the following exercises, solve.

Robin deposited $31,000 in a bank account with interest rate 5.2%. How much interest was earned in 3 years?

Solve Simple Interest Applications

In the following exercises, solve.

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 interest?

Solve Simple Interest Applications

In the following exercises, solve.

Lebron loaned 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 interest?

Solve Simple Interest Applications

In the following exercises, solve.

In 10 years, a bank account that paid 5.25% earned $18,375 interest. What was the principal of the account?

Solve Simple Interest Applications

In the following exercises, solve.

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

Solve Applications with Discount or Mark-up

In the following exercises, find the sale price.

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

Solve Applications with Discount or Mark-up

In the following exercises, find the sale price.

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

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.

In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.

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

In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.

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

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.

In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)

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

In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)

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?

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%.

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

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

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

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

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

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?

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

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.

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

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

Multiply: 14(0.25).
If you missed this problem, review Example 1.97.

Solve: $0.25x+$ $0.10(x+4)=$ $2.5.$
If you missed this problem, review Example 2.44.

The number of dimes is three more than the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.
If you missed this problem, review Example 1.26.

Michaela has $2.05 in dimes and nickels in her change purse. She has seven more dimes than nickels. How many coins of each type does she have?

Liliana has $2.10 in nickels and quarters in her backpack. She has 12 more nickels than quarters. How many coins of each type does she have?

Sumanta has $4.20 in nickels and dimes in her piggy bank. She has twice as many nickels as dimes. How many coins of each type does she have?

Alison has three times as many dimes as quarters in her purse. She has $9.35 altogether. How many coins of each type does she have?

Jesse has $6.55 worth of quarters and nickels in his pocket. The number of nickels is five more than two times the number of quarters. How many nickels and how many quarters does Jesse have?

Elane has $7.00 total in dimes and nickels in her coin jar. The number of dimes that Elane has is seven less than three times the number of nickels. How many of each coin does Elane have?

The first day of a water polo tournament the total value of tickets sold was $17,610. One-day passes sold for $20 and tournament passes sold for $30. The number of tournament passes sold was 37 more than the number of day passes sold. How many day passes and how many tournament passes were sold?

At the movie theater, the total value of tickets sold was $2,612.50. Adult tickets sold for $10 each and senior/child tickets sold for $7.50 each. The number of senior/child tickets sold was 25 less than twice the number of adult tickets sold. How many senior/child tickets and how many adult tickets were sold?

During her shift at the museum ticket booth, Leah sold 115 tickets for a total of $1,163. Adult tickets cost $12 and student tickets cost $5. How many adult tickets and how many student tickets did Leah sell?

A whale-watching ship had 40 paying passengers on board. The total collected from tickets was $1,196. Full-fare passengers paid $32 each and reduced-fare passengers paid $26 each. How many full-fare passengers and how many reduced-fare passengers were on the ship?

Eric paid $13.36 for stamps. The number of 41-cent stamps was eight more than twice the number of two-cent stamps. How many 41-cent stamps and how many two-cent stamps did Eric buy?

Kailee paid $12.66 for stamps. The number of 41-cent stamps was four less than three times the number of 20-cent stamps. How many 41-cent stamps and how many 20-cent stamps did Kailee buy?

Orlando is mixing nuts and cereal squares to make a party mix. Nuts sell for $7 a pound and cereal squares sell for $4 a pound. Orlando wants to make 30 pounds of party mix at a cost of $6.50 a pound, how many pounds of nuts and how many pounds of cereal squares should he use?

Becca wants to mix fruit juice and soda to make a punch. She can buy fruit juice for $3 a gallon and soda for $4 a gallon. If she wants to make 28 gallons of punch at a cost of $3.25 a gallon, how many gallons of fruit juice and how many gallons of soda should she buy?

Remy has $14,000 to invest in two mutual funds. One fund pays interest at 4% per year and the other fund pays interest at 7% per year. How much should she invest in each fund if she wants to earn 6.1% interest on the total amount?

Marco has $8,000 to save for his daughter’s college education. He wants to divide it between one account that pays 3.2% interest per year and another account that pays 8% interest per year. How much should he invest in each account if he wants the interest on the total investment to be 6.5%?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Jaime has $2.60 in dimes and nickels. The number of dimes is 14 more than the number of nickels. How many of each coin does he have?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Ngo has a collection of dimes and quarters with a total value of $3.50. The number of dimes is seven more than the number of quarters. How many of each coin does he have?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

A cash box of $1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. How many of each bill does it contain?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Rachelle has $6.30 in nickels and quarters in her coin purse. The number of nickels is twice the number of quarters. How many coins of each type does she have?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Harrison has $9.30 in his coin collection, all in pennies and dimes. The number of dimes is three times the number of pennies. How many coins of each type does he have?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

In a cash drawer there is $125 in $5 and $10 bills. The number of $10 bills is twice the number of $5 bills. How many of each are in the drawer?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Carolyn has $2.55 in her purse in nickels and dimes. The number of nickels is nine less than three times the number of dimes. Find the number of each type of coin.

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Chi has $11.30 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many of each are there?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

Mukul has $3.75 in quarters, dimes and nickels in his pocket. He has five more dimes than quarters and nine more nickels than quarters. How many of each coin are in his pocket?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

The school play sold $550 in tickets one night. The number of $8 adult tickets was 10 less than twice the number of $5 child tickets. How many of each ticket were sold?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

The movie theater took in $1,220 one Monday night. The number of $7 child tickets was ten more than twice the number of $9 adult tickets. How many of each were sold?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

The box office sold 360 tickets to a concert at the college. The total receipts were $4170. General admission tickets cost $15 and student tickets cost $10. How many of each kind of ticket was sold?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

Julie went to the post office and bought both $0.41 stamps and $0.26 postcards. She spent $51.40. The number of stamps was 20 more than twice the number of postcards. How many of each did she buy?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

Maria spent $12.50 at the post office. She bought three times as many $0.41 stamps as $0.02 stamps. How many of each did she buy?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

Hilda has $210 worth of $10 and $12 stock shares. The numbers of $10 shares is five more than twice the number of $12 shares. How many of each does she have?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

Lauren in making 15 liters of mimosas for a brunch banquet. Orange juice costs her $1.50 per liter and champagne costs her $12 per liter. How many liters of orange juice and how many liters of champagne should she use for the mimosas to cost Lauren $5 per liter?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

Kaapo is mixing Kona beans and Maui beans to make 25 pounds of coffee blend. Kona beans cost Kaapo $15 per pound and Maui beans cost $24 per pound. How many pounds of each coffee bean should Kaapo use for his blend to cost him $17.70 per pound?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

Carmen wants to tile the floor of his house. He will need 1000 square feet of tile. He will do most of the floor with a tile that costs $1.50 per square foot, but also wants to use an accent tile that costs $9.00 per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be $3 per square foot?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

Vartan was paid $25,000 for a cell phone app that he wrote and wants to invest it to save for his son’s education. He wants to put some of the money into a bond that pays 4% annual interest and the rest into stocks that pay 9% annual interest. If he wants to earn 7.4% annual interest on the total amount, how much money should he invest in each account?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

Stephanie inherited $40,000. She wants to put some of the money in a certificate of deposit that pays 2.1% interest per year and the rest in a mutual fund account that pays 6.5% per year. How much should she invest in each account if she wants to earn 5.4% interest per year on the total amount?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

Dominic pays 7% interest on his $15,000 college loan and 12% interest on his $11,000 car loan. What average interest rate does he pay on the total $26,000 he owes? (Round your answer to the nearest tenth of a percent.)

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

As the treasurer of her daughter’s Girl Scout troop, Laney collected money for some girls and adults to go to a 3-day camp. Each girl paid $75 and each adult paid $30. The total amount of money collected for camp was $765. If the number of girls is three times the number of adults, how many girls and how many adults paid for camp?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

Suppose you have six quarters, nine dimes, and four pennies. Explain how you find the total value of all the coins.

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

In the table used to solve coin problems, one column is labeled “number” and another column is labeled “value.” What is the difference between the “number” and the “value?”

Simplify: $\frac{1}{2}(6h).$
If you missed this problem, review Example 1.122.

The length of a rectangle is three less than the width. Let w represent the width. Write an expression for the length of the rectangle.
If you missed this problem, review Example 1.26.

Solve: $A=\frac{1}{2}bh$ for b when $A=260$ and $h=52.$
If you missed this problem, review Example 2.61.

Simplify: $\sqrt{144}.$
If you missed this problem, review Example 1.111.

The measures of two angles of a triangle are 31 and 128 degrees. Find the measure of the third angle.

The measures of two angles of a triangle are 49 and 75 degrees. Find the measure of the third angle.

The perimeter of a triangular garden is 48 feet. The lengths of two sides are 18 feet and 22 feet. How long is the third side?

The lengths of two sides of a triangular window are seven feet and five feet. The perimeter is 18 feet. How long is the third side?

The area of a triangular painting is 126 square inches. The base is 18 inches. What is the height?

A triangular tent door has an area of 15 square feet. The height is five feet. What is the base?

One angle of a right triangle measures $56\text{°}.$ What is the measure of the other small angle?

One angle of a right triangle measures $45\text{°}.$ What is the measure of the other small angle?

The measure of one angle of a right triangle is 50° more than the measure of the smallest angle. Find the measures of all three angles.

The measure of one angle of a right triangle is 30° more than the measure of the smallest angle. Find the measures of all three angles.

Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.

Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.

Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.

Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.

John puts the base of a 13-foot ladder five feet from the wall of his house as shown below. How far up the wall does the ladder reach?

Randy wants to attach a 17 foot string of lights to the top of the 15 foot mast of his sailboat, as shown below. How far from the base of the mast should he attach the end of the light string?

The length of a rectangle is 120 yards and the width is 50 yards. What is the perimeter?

The length of a rectangle is 62 feet and the width is 48 feet. What is the perimeter?

The area of a rectangle is 598 square feet. The length is 23 feet. What is the width?

The width of a rectangle is 21 meters. The area is 609 square meters. What is the length?

Find the length of a rectangle with: perimeter 80 and width 25.

Find the length of a rectangle with: perimeter 30 and width 6.

The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.

The length of a rectangle is eight feet more than the width. The perimeter is 60 feet. Find the length and width.

The length of a rectangle is eight more than twice the width. The perimeter is 64. Find the length and width.

The width of a rectangle is six less than twice the length. The perimeter is 18. Find the length and width.

The perimeter of a rectangular swimming pool is 200 feet. The length is 40 feet more than the width. Find the length and width.

The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width.

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

The measures of two angles of a triangle are 26 and 98 degrees. Find the measure of the third angle.

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

The measures of two angles of a triangle are 105 and 31 degrees. Find the measure of the third angle.

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

The perimeter of a triangular pool is 36 yards. The lengths of two sides are 10 yards and 15 yards. How long is the third side?

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

If a triangle has sides 6 feet and 9 feet and the perimeter is 23 feet, how long is the third side?

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

A triangular flag has base one foot and height 1.5 foot. What is its area?

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

What is the base of a triangle with area 207 square inches and height 18 inches?

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

One angle of a right triangle measures 33 degrees. What is the measure of the other small angle?

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

One angle of a right triangle measures 22.5 degrees. What is the measure of the other small angle?

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

The perimeter of a triangle is 39 feet. One side of the triangle is one foot longer than the second side. The third side is two feet longer than the second side. Find the length of each side.

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

One side of a triangle is twice the shortest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.

Solving Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

The angles in a triangle are such that one angle is twice the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.

Use the Pythagorean Theorem

In the following exercises, use the Pythagorean Theorem to find the length of the hypotenuse.

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 leg. Round to the nearest tenth, if necessary.

In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary.

In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary.

In the following exercises, use the Pythagorean Theorem to find the length of the leg. Round to the nearest tenth, if necessary.

In the following exercises, solve using the Pythagorean Theorem. Approximate to the nearest tenth, if necessary.

A 13-foot string of lights will be attached to the top of a 12-foot pole for a holiday display, as shown below. How far from the base of the pole should the end of the string of lights be anchored?

In the following exercises, solve using the Pythagorean Theorem. Approximate to the nearest tenth, if necessary.

Chi is planning to put a path of paving stones through her flower garden, as shown below. The flower garden is a square with side 10 feet. What will the length of the path be?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The length of a rectangle is 85 feet and the width is 45 feet. What is the perimeter?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

A rectangular room is 15 feet wide by 14 feet long. What is its perimeter?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The area of a rectangle is 414 square meters. The length is 18 meters. What is the width?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The width of a rectangular window is 24 inches. The area is 624 square inches. What is the length?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

Find the length of a rectangle with perimeter 124 and width 38.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

Find the width of a rectangle with perimeter 16.2 and length 3.2.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The length of a rectangle is nine inches more than the width. The perimeter is 46 inches. Find the length and the width.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The perimeter of a rectangle is 58 meters. The width of the rectangle is five meters less than the length. Find the length and the width of the rectangle.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The width of the rectangle is 0.7 meters less than the length. The perimeter of a rectangle is 52.6 meters. Find the dimensions of the rectangle.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The perimeter of a rectangle is 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The length of a rectangle is three meters less than twice the width. The perimeter of the rectangle is 36 meters. Find the dimensions of the rectangle.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The perimeter of a rectangular field is 560 yards. The length is 40 yards more than the width. Find the length and width of the field.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

A rectangular parking lot has perimeter 250 feet. The length is five feet more than twice the width. Find the length and width of the parking lot.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are six feet, eight feet and 10 feet. How many feet of fencing will she need to enclose her flowerbed?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

Look at the two figures below.

ⓐ Which figure looks like it has the larger area?

ⓑ Which looks like it has the larger perimeter?

ⓒ Now calculate the area and perimeter of each figure.

ⓓ Which has the larger area?

ⓔ Which has the larger perimeter?

Find the distance travelled by a car going 70 miles per hour for 3 hours.
If you missed this problem, review Example 2.58.

Solve $x+$ $1.2(x-10)=$ $98.$
If you missed this problem, review Example 2.39.

Convert 90 minutes to hours.
If you missed this problem, review Example 1.140.

Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.

Jeromy can drive from his house in Cleveland to his college in Chicago in 4.5 hours. It takes his mother 6 hours to make the same drive. Jeromy drives 20 miles per hour faster than his mother. Find Jeromy’s speed and his mother’s speed.

Carina is driving from her home in Anaheim to Berkeley on the same day her brother is driving from Berkeley to Anaheim, so they decide to meet for lunch along the way in Buttonwillow. The distance from Anaheim to Berkeley is 410 miles. It takes Carina 3 hours to get to Buttonwillow, while her brother drives 4 hours to get there. The average speed Carina’s brother drove was 15 miles per hour faster than Carina’s average speed. Find Carina’s and her brother’s average speeds.

Ashley goes to college in Minneapolis, 234 miles from her home in Sioux Falls. She wants her parents to bring her more winter clothes, so they decide to meet at a restaurant on the road between Minneapolis and Sioux Falls. Ashley and her parents both drove 2 hours to the restaurant. Ashley’s average speed was seven miles per hour faster than her parents’ average speed. Find Ashley’s and her parents’ average speed.

Pierre and Monique leave their home in Portland at the same time. Pierre drives north on the turnpike at a speed of 75 miles per hour while Monique drives south at a speed of 68 miles per hour. How long will it take them to be 429 miles apart?

Thanh and Nhat leave their office in Sacramento at the same time. Thanh drives north on I-5 at a speed of 72 miles per hour. Nhat drives south on I-5 at a speed of 76 miles per hour. How long will it take them to be 330 miles apart?

Suzy takes 50 minutes to hike uphill from the parking lot to the lookout tower. It takes her 30 minutes to hike back down to the parking lot. Her speed going downhill is 1.2 miles per hour faster than her speed going uphill. Find Suzy’s uphill and downhill speeds.

Llewyn takes 45 minutes to drive his boat upstream from the dock to his favorite fishing spot. It takes him 30 minutes to drive the boat back downstream to the dock. The boat’s speed going downstream is four miles per hour faster than its speed going upstream. Find the boat’s upstream and downstream speeds.

Cruz is training to compete in a triathlon. He left his house at 6:00 and ran until 7:30. Then he rode his bike until 9:45. He covered a total distance of 51 miles. His speed when biking was 1.6 times his speed when running. Find Cruz’s biking and running speeds.

Phuong left home on his bicycle at 10:00. He rode on the flat street until 11:15, then rode uphill until 11:45. He rode a total of 31 miles. His speed riding uphill was 0.6 times his speed on the flat street. Find his speed biking uphill and on the flat street.

Solve Uniform Motion Applications

In the following exercises, solve.

Lilah is moving from Portland to Seattle. It takes her three hours to go by train. Mason leaves the train station in Portland and drives to the train station in Seattle with all Lilah’s boxes in his car. It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the speed of the train. Find Mason’s speed and the speed of the train.

Solve Uniform Motion Applications

In the following exercises, solve.

Two busses go from Sacramento for San Diego. The express bus makes the trip in 6.8 hours and the local bus takes 10.2 hours for the trip. The speed of the express bus is 25 mph faster than the speed of the local bus. Find the speed of both busses.

Solve Uniform Motion Applications

In the following exercises, solve.

Saul drove his truck 3 hours from Dallas towards Kansas City and stopped at a truck stop to get dinner. At the truck stop he met Erwin, who had driven 4 hours from Kansas City towards Dallas. The distance between Dallas and Kansas City is 542 miles, and Erwin’s speed was eight miles per hour slower than Saul’s speed. Find the speed of the two truckers.

Solve Uniform Motion Applications

In the following exercises, solve.

Sisters Helen and Anne live 332 miles apart. For Thanksgiving, they met at their other sister’s house partway between their homes. Helen drove 3.2 hours and Anne drove 2.8 hours. Helen’s average speed was four miles per hour faster than Anne’s. Find Helen’s average speed and Anne’s average speed.

Solve Uniform Motion Applications

In the following exercises, solve.

Elvira and Aletheia live 3.1 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira half an hour and Aletheia two-thirds of an hour to walk to the coffee shop. Aletheia’s speed is 0.6 miles per hour slower than Elvira’s speed. Find both women’s walking speeds.

Solve Uniform Motion Applications

In the following exercises, solve.

Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?

Solve Uniform Motion Applications

In the following exercises, solve.

Two busses leave Billings at the same time. The Seattle bus heads west on I-90 at a speed of 73 miles per hour while the Chicago bus heads east at a speed of 79 miles an hour. How many hours will it take them to be 532 miles apart?

Solve Uniform Motion Applications

In the following exercises, solve.

Lorena walks the path around the park in 30 minutes. If she jogs, it takes her 20 minutes. Her jogging speed is 1.5 miles per hour faster than her walking speed. Find Lorena’s walking speed and jogging speed.

Solve Uniform Motion Applications

In the following exercises, solve.

Cassius drives his boat upstream for 45 minutes. It takes him 30 minutes to return downstream. His speed going upstream is three miles per hour slower than his speed going downstream. Find his upstream and downstream speeds.

Solve Uniform Motion Applications

In the following exercises, solve.

At 1:30 Marlon left his house to go to the beach, a distance of 7.6 miles. He rode his skateboard until 2:15, then walked the rest of the way. He arrived at the beach at 3:00. Marlon’s speed on his skateboard is 2.5 times his walking speed. Find his speed when skateboarding and when walking.

Solve Uniform Motion Applications

In the following exercises, solve.

Marisol left Los Angeles at 2:30 to drive to Santa Barbara, a distance of 95 miles. The traffic was heavy until 3:20. She drove the rest of the way in very light traffic and arrived at 4:20. Her speed in heavy traffic was 40 miles per hour slower than her speed in light traffic. Find her speed in heavy traffic and in light traffic.

Solve Uniform Motion Applications

In the following exercises, solve.

John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.

ⓐ What was his average speed on the drive from Irvine to Los Angeles?

ⓑ What was his average speed on the drive from Los Angeles to Irvine?

ⓒ What was the total time he spent driving to and from this meeting?

ⓓ John drove a total of 90 miles roundtrip. Find his average speed. (Round to the nearest tenth.)

Solve Uniform Motion Applications

In the following exercises, solve.

When solving a uniform motion problem, how does drawing a diagram of the situation help you?

Write as an inequality: x is at least 30.
If you missed this problem, review Example 2.77.

Solve $8-3y<41.$
If you missed this problem, review Example 2.73.

Alan is loading a pallet with boxes that each weighs 45 pounds. The pallet can safely support no more than 900 pounds. How many boxes can he safely load onto the pallet?

The elevator in Yehire’s apartment building has a sign that says the maximum weight is 2,100 pounds. If the average weight of one person is 150 pounds, how many people can safely ride the elevator?

Angie has $20 to spend on juice boxes for her son’s preschool picnic. Each pack of juice boxes costs $2.63. What is the maximum number of packs she can buy?

Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. It will cost $42.75 per person for dinner, including tip and tax. His budget for the party is $500. What is the maximum number of people Daniel can have at the party?

Tiffany just graduated from college and her new job will pay her $20,000 per year plus 2% of all sales. She wants to earn at least $100,000 per year. For what total sales will she be able to achieve her goal?

Christian has been offered a new job that pays $24,000 a year plus 3% of sales. For what total sales would this new job pay more than his current job which pays $60,000?

Taleisha’s phone plan costs her $28.80 a month plus $0.20 per text message. How many text messages can she use and keep her monthly phone bill no more than $50?

Rameen’s heating bill is $5.42 per month plus $1.08 per therm. How many therms can Rameen use if he wants his heating bill to be a maximum of $87.50?

Caleb has a pet sitting business. He charges $32 per hour. His monthly expenses are $2,272. How many hours must he work in order to earn a profit of at least $800 per month?

Felicity has a calligraphy business. She charges $2.50 per wedding invitation. Her monthly expenses are $650. How many invitations must she write to earn a profit of at least $2,800 per month?

Malik is planning a 6-day summer vacation trip. He has $840 in savings, and he earns $45 per hour for tutoring. The trip will cost him $525 for airfare, $780 for food and sightseeing, and $95 per night for the hotel. How many hours must he tutor to have enough money to pay for the trip?

Josue wants to go on a 10-day road trip next spring. It will cost him $180 for gas, $450 for food, and $49 per night for a motel. He has $520 in savings and can earn $30 per driveway shoveling snow. How many driveways must he shovel to have enough money to pay for the trip?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Mona is planning her son’s birthday party and has a budget of $285. The Fun Zone charges $19 per child. How many children can she have at the party and stay within her budget?

Solve Applications with Linear Inequalities

In the following exercises, solve.

A water taxi has a maximum load of 1,800 pounds. If the average weight of one person is 150 pounds, how many people can safely ride in the water taxi?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Arleen got a $20 gift card for the coffee shop. Her favorite iced drink costs $3.79. What is the maximum number of drinks she can buy with the gift card?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Joni sells kitchen aprons online for $32.50 each. How many aprons must she sell next month if she wants to earn at least $1,000?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Keshad gets paid $2,400 per month plus 6% of his sales. His brother earns $3,300 per month. For what amount of total sales will Keshad’s monthly pay be higher than his brother’s monthly pay?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Andre has been offered an entry-level job. The company offered him $48,000 per year plus 3.5% of his total sales. Andre knows that the average pay for this job is $62,000. What would Andre’s total sales need to be for his pay to be at least as high as the average pay for this job?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Jake’s water bill is $24.80 per month plus $2.20 per ccf (hundred cubic feet) of water. What is the maximum number of ccf Jake can use if he wants his bill to be no more than $60?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Marlon’s TV plan costs $49.99 per month plus $5.49 per first-run movie. How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of $100?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Moshde runs a hairstyling business from her house. She charges $45 for a haircut and style. Her monthly expenses are $960. She wants to be able to put at least $1,200 per month into her savings account order to open her own salon. How many “cut & styles” must she do to save at least $1,200 per month?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Katherine is a personal chef. She charges $115 per four-person meal. Her monthly expenses are $3,150. How many four-person meals must she sell in order to make a profit of at least $1,900?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Five student government officers want to go to the state convention. It will cost them $110 for registration, $375 for transportation and food, and $42 per person for the hotel. There is $450 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Alonzo works as a car detailer. He charges $175 per car. He is planning to move out of his parents’ house and rent his first apartment. He will need to pay $120 for application fees, $950 for security deposit, and first and last months’ rent at $1,140 per month. He has $1,810 in savings. How many cars must he detail to have enough money to rent the apartment?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Maximum Load on a Stage In 2014, a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production. Two dozen students were injured. The stage could support a maximum of 12,750 pounds. If the average weight of a student is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Wedding Budget Adele and Walter found the perfect venue for their wedding reception. The cost is $9,850 for up to 100 guests, plus $38 for each additional guest. How many guests can attend if Adele and Walter want the total cost to be no more than $12,500?

Solve Applications with Linear Inequalities

In the following exercises, solve.

Find your last month’s phone bill and the hourly salary you are paid at your job. (If you do not have a job, use the hourly salary you would realistically be paid if you had a job.) Calculate the number of hours of work it would take you to earn at least enough money to pay your phone bill by writing an appropriate inequality and then solving it.

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.

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?

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.

Solve Number Problems

In the following exercises, solve each number word problem.

One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.

Solve Number Problems

In the following exercises, solve each number word problem.

One number is two more than four times another. Their sum is $\mathrm{-13}.$ Find the numbers.

Solve Number Problems

In the following exercises, solve each number word problem.

Find three consecutive integers whose sum is $\mathrm{-141}.$

Solve Number Problems

In the following exercises, solve each number word problem.

Find three consecutive odd integers whose sum is 51.

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What number is 67% of 250?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

12.5% of what number is 20?

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

What percent of 125 is 150?

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?

Solve Percent Applications

In the following exercises, solve.

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?

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.

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?

Solve Simple Interest Applications

In the following exercises, solve.

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?

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.

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.

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.

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.

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?

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

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?

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?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

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?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

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?

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?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

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?

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.

Solve Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

A triangular road sign has base 30 inches and height 40 inches. What is its area?

Solve Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

One angle of a triangle is $30\text{°}$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.

Solve Applications Using Triangle Properties

In the following exercises, solve using triangle properties.

The measure of the smallest angle in a right triangle is $45\text{°}$ less than the measure of the next larger angle. Find the measures of all three angles.

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, 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?

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.

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The area of a rectangle is 2356 square meters. The length is 38 meters. What is the width?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The length of a rectangle is 12 cm more than the width. The perimeter is 74 cm. Find the length and the width.

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.

Solve Uniform Motion Applications

In the following exercises, solve.

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?

Solve Uniform Motion Applications

In the following exercises, solve.

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.

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?

Solve Applications with Linear Inequalities

In the following exercises, solve.

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?

Solve Applications with Linear Inequalities

In the following exercises, solve.

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?

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?

The sum of two consecutive odd integers is $\mathrm{-96}.$ Find the numbers.

Humberto’s hourly pay increased from $16.25 to $17.55. Find the percent increase.

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.

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?

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.

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, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

A baseball diamond is really a square with sides of 90 feet. How far is it from home plate to second base, as shown?

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

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?

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Chloe has a budget of $800 for costumes for the 18 members of her musical theater group. If all the costumes are the same price, what is the maximum she can spend for each costume?