Math Word Problems Demystified - A Self Teaching Guide

In order to avoid decimals, it is easier to work with cents rather than
dollars. You can change dollars to cents by multiplying by 100. You can
change the answer back to dollars by dividing by 100.

EXAMPLE:A person has 8 coins consisting of quarters and dimes. If the
total amount of this change is $1.25, how many of each kind of coin are
there?

SOLUTION:

GOAL: You are being asked to find the number of quarters and the number
of dimes the person has.

STRATEGY: Letx¼the number of quarters and (8
x)¼the number of
dimes; then the value of the quarters is 25xand the value of the dimes is
10(8
x). The total amount of money in cents is $1.25 100 ¼ 125 c. The
equation is 25xþ10(8
x)¼125.

IMPLEMENTATION: Solve the equation:

25 xþ 10 ð 8 
xÞ¼ 125

25 xþ 80 
 10 x¼ 125

15 xþ 80 ¼ 125

15 xþ 80 
 80 ¼ 125 
 80

15 x¼ 45

151 x

151

¼

45

15

x¼3 (quarters)

8 
x¼ 8 
 3 ¼5 (dimes)

There are 3 quarters and 5 dimes.

EVALUATION: The value of 3 quarters and 5 dimes is 3 25 cþ
5  10 c¼ 75 cþ 50 c¼ 125 c¼$1.25.

LESSON 11 Solving Coin Problems 109