Math Word Problems Demystified - A Self Teaching Guide

EXAMPLE:A person has 3 times as many dimes as he has nickels and 5

more pennies than nickels. If the total amount of these coins is $1.13, how

many of each kind of coin does he have?

SOLUTION:

GOAL: You are being asked to find the number of nickels, pennies, and

dimes.

STRATEGY: Letx¼the number of nickels, 3x¼the number of dimes, and

xþ 5 ¼the number of pennies. Then the value of the nickels is 5x. The value

of the dimes is 10 3 xor 30x. The value of the pennies is 1(xþ5). The total

amount is $1.13100 or 113c. The equation is 5xþ 30 xþ(xþ5)¼113.

IMPLEMENTATION: Solve the equation:

5 xþ 30 xþðxþ 5 Þ¼ 113

5 xþ 30 xþxþ 5 ¼ 113

36 xþ 5 ¼ 113

36 xþ 5 
 5 ¼ 113 
 5

36 x¼ 108

361 x

361

¼

108

36

x¼3 (nickels)

3 x¼ 3  3 ¼9 (dimes)

xþ 5 ¼ 3 þ 5 ¼8 (pennies)

There are 3 nickels, 9 dimes, and 8 pennies.

EVALUATION: The value of 3 nickels, 9 dimes, and 8 pennies is

3  5 cþ 9  10 cþ 8  1 c¼ 15 cþ 90 cþ 8 c¼ 113 c or $1.13.

Other types of problems involving values can be solved using the same

strategy as the coin problems. Consider the next example.

110 LESSON 11 Solving Coin Problems