Intermediate Algebra (11th edition)

Solving a Money Denomination Problem

For a bill totaling $5.65, a cashier received 25 coins consisting of nickels and quar-

ters. How many of each denomination of coin did the cashier receive?

Step 1 Readthe problem. The problem asks that we find the number of nickels and

the number of quarters the cashier received.

Step 2 Assign a variable.Then organize the information in a table.

Let the number of nickels.

Then 25 - x= the number of quarters.

x=

EXAMPLE 1

SECTION 2.4 Further Applications of Linear Equations 81

OBJECTIVES

Further Applications of Linear Equations

2.4

1 Solve problems

about different

denominations

of money.

2 Solve problems

about uniform

motion.

3 Solve problems

about angles.

OBJECTIVE 1 Solve problems about different denominations of money.

CAUTION Be sure that your answer is reasonablewhen you are working prob-

lems like Example 1.Because you are dealing with a number of coins, the correct

answer can be neither negative nor a fraction.

In problems involving money, use the following basic fact.

number of monetary total monetary

units of the same kind

denomination

value

30 dimes have a monetary value of

Fifteen 5-dollar bills have a value of 15 1 $5 2 =$75.

301 $0.10 2 =$3.00.

: 

PROBLEM-SOLVING HINT

Number of Coins Denomination Value

Nickels x 0.05 0.05x

Quarters 0.25

5.65 Total

25 - x 0.25 125 - x 2

Step 3 Write an equationfrom the last column of the table.

Step 4 Solve.

Multiply by 100.

Distributive property

Subtract 625. Combine like terms.

x= 3 Divide by -20.

- 20 x=- 60

5 x+ 625 - 25 x= 565

5 x+ 25125 - x 2 = 565

0.05x+0.25 125 - x 2 =5.65

0.05x+ 0.25 125 - x 2 =5.65

Move decimal

points 2 places

to the right.

Step 5 State the answer.The cashier has 3 nickels and quarters.

Step 6 Check.The cashier has and the value of the coins is

$0.05 132 +$0.25 1222 =$5.65, as required. NOW TRY

3 + 22 =25 coins,

25 - 3 = 22

NOW TRY
EXERCISE 1
Steven Danielson has a col-
lection of 52 coins worth
$3.70. His collection contains
only dimes and nickels. How
many of each type of coin
does he have?

NOW TRY ANSWER

1. 22 dimes; 30 nickels