# 3.4E: Exercises

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- Contributed by Lynn Marecek
- Professor (Mathematics) at Santa Ana College
- Publisher: OpenStax CNX

### Practice Makes Perfect

**Solve Coin Word Problems**

In the following exercises, solve each coin word problem.

Exercise \(\PageIndex{1}\)

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?

**Answer**-
8 nickels, 22 dimes

Exercise \(\PageIndex{2}\)

Lee has $1.75 in dimes and nickels. The number of nickels is 11 more than the number of dimes. How many of each coin does he have?

Exercise \(\PageIndex{3}\)

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?

**Answer**-
15 dimes, 8 quarters

Exercise \(\PageIndex{4}\)

Connor has a collection of dimes and quarters with a total value of $6.30. The number of dimes is 14 more than the number of quarters. How many of each coin does he have?

Exercise \(\PageIndex{5}\)

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?

**Answer**-
10 at $1, 7 at $5

Exercise \(\PageIndex{6}\)

Joe’s wallet contains $1 and $5 bills worth $47. The number of $1 bills is five more than the number of $5 bills. How many of each bill does he have?

Exercise \(\PageIndex{7}\)

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?

**Answer**-
18 quarters, 36 nickels

Exercise \(\PageIndex{8}\)

Deloise has $1.20 in pennies and nickels in a jar on her desk. The number of pennies is three times the number of nickels. How many coins of each type does she have?

Exercise \(\PageIndex{9}\)

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?

**Answer**-
30 pennies, 90 dimes

Exercise \(\PageIndex{10}\)

Ivan has $8.75 in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have?

Exercise \(\PageIndex{11}\)

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?

**Answer**-
10 at $10, 5 at $5

Exercise \(\PageIndex{12}\)

John has $175 in $5 and $10 bills in his drawer. The number of $5 bills is three times the number of $10 bills. How many of each are in the drawer?

Exercise \(\PageIndex{13}\)

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.

**Answer**-
12 dimes and 27 nickels

Exercise \(\PageIndex{14}\)

Julio has $2.75 in his pocket in nickels and dimes. The number of dimes is 10 less than twice the number of nickels. Find the number of each type of coin.

Exercise \(\PageIndex{15}\)

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?

**Answer**-
63 dimes, 20 quarters

Exercise \(\PageIndex{16}\)

Tyler has $9.70 in dimes and quarters. The number of quarters is eight more than four times the number of dimes. How many of each coin does he have?

Exercise \(\PageIndex{17}\)

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?

**Answer**-
16 nickels, 12 dimes, 7 quarters

Exercise \(\PageIndex{18}\)

Vina has $4.70 in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin are in her purse?

**Solve Ticket and Stamp Word Problems**

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

Exercise \(\PageIndex{19}\)

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?

**Answer**-
30 child tickets, 50 adult tickets

Exercise \(\PageIndex{20}\)

If the number of $8 child tickets is seventeen less than three times the number of $12 adult tickets and the theater took in $584, how many of each ticket were sold?

Exercise \(\PageIndex{21}\)

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?

**Answer**-
110 child tickets, 50 adult tickets

Exercise \(\PageIndex{22}\)

The ball game sold $1,340 in tickets one Saturday. The number of $12 adult tickets was 15 more than twice the number of $5 child tickets. How many of each were sold?

Exercise \(\PageIndex{23}\)

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?

**Answer**-
34 general, 61 youth

Exercise \(\PageIndex{24}\)

For the 7:30 show time, 140 movie tickets were sold. Receipts from the $13 adult tickets and the $10 senior tickets totaled $1,664. How many adult tickets and how many senior tickets were sold?

Exercise \(\PageIndex{25}\)

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?

**Answer**-
114 general, 246 student

Exercise \(\PageIndex{26}\)

Last Saturday, the museum box office sold 281 tickets for a total of $3954. Adult tickets cost $15 and student tickets cost $12. How many of each kind of ticket was sold?

Exercise \(\PageIndex{27}\)

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?

**Answer**-
40 postcards, 100 stamps

Exercise \(\PageIndex{28}\)

Jason went to the post office and bought both $0.41 stamps and $0.26 postcards and spent $10.28. The number of stamps was four more than twice the number of postcards. How many of each did he buy?

Exercise \(\PageIndex{29}\)

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?

**Answer**-
30 at $0.41, 10 at $0.02

Exercise \(\PageIndex{30}\)

Hector spent $33.20 at the post office. He bought four times as many $0.41 stamps as $0.02 stamps. How many of each did he buy?

Exercise \(\PageIndex{31}\)

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?

**Answer**-
15 $10 shares, 5 $12 shares

Exercise \(\PageIndex{32}\)

Mario invested $475 in $45 and $25 stock shares. The number of $25 shares was five less than three times the number of $45 shares. How many of each type of share did he buy?

**Solve Mixture Word Problems**

In the following exercises, solve each mixture word problem.

Exercise \(\PageIndex{33}\)

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?

**Answer**-
5 liters champagne, 10 liters orange juice

Exercise \(\PageIndex{34}\)

Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. How many pounds of macadamia nuts and how many pounds of almonds should Macario use for the mixture to cost $6.50 per pound to make?

Exercise \(\PageIndex{35}\)

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?

**Answer**-
7.5 lbs Maui beans, 17.5 Kona beans

Exercise \(\PageIndex{36}\)

Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound and blueberries cost $4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use?

Exercise \(\PageIndex{37}\)

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?

**Answer**-
800 at $1.50, 200 at $9.00

Exercise \(\PageIndex{38}\)

Riley is planning to plant a lawn in his yard. He will need nine pounds of grass seed. He wants to mix Bermuda seed that costs $4.80 per pound with Fescue seed that costs $3.50 per pound. How much of each seed should he buy so that the overall cost will be $4.02 per pound?

Exercise \(\PageIndex{39}\)

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?

**Answer**-
$8000 at 4%, $17,000 at 9%

Exercise \(\PageIndex{40}\)

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 5.8% interest per year. He will put some of the money into Fund A that earns 3% per year and the rest in Fund B that earns 10% per year. How much should he invest into each fund if he wants to earn 5.8% interest per year on the total amount?

Exercise \(\PageIndex{41}\)

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?

**Answer**-
$10,000 in CD, $30,000 in mutual fund

Exercise \(\PageIndex{42}\)

Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year?

Exercise \(\PageIndex{43}\)

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.)

**Answer**-
9.1%

Exercise \(\PageIndex{44}\)

Liam borrowed a total of $35,000 to pay for college. He pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total $35,000? (Round your answer to the nearest tenth of a percent.)

### Everyday Math

Exercise \(\PageIndex{45}\)

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?

**Answer**-
9 girls, 3 adults

Exercise \(\PageIndex{46}\)

Laurie was completing the treasurer’s report for her son’s Boy Scout troop at the end of the school year. She didn’t remember how many boys had paid the $15 full-year registration fee and how many had paid the $10 partial-year fee. She knew that the number of boys who paid for a full-year was ten more than the number who paid for a partial-year. If $250 was collected for all the registrations, how many boys had paid the full-year fee and how many had paid the partial-year fee?

### Writing Exercises

Exercise \(\PageIndex{47}\)

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

**Answer**-
Answers will vary.

Exercise \(\PageIndex{48}\)

Do you find it helpful to use a table when solving coin problems? Why or why not?

Exercise \(\PageIndex{49}\)

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?”

**Answer**-
Answers will vary.

Exercise \(\PageIndex{50}\)

What similarities and differences did you see between solving the coin problems and the ticket and stamp problems?

### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?