Math Word Problems Demystified - A Self Teaching Guide

EXAMPLE:The sum of the digits of a two-digit number is 15. If the digits
are reversed, the new number is 9 more than the original number. Find the
number.

SOLUTION:

GOAL: You are being asked to find a certain two-digit number.

STRATEGY: Letx¼the ten’s digit and 15
x¼the one’s digit. The original
number can be written as 10xþ(15
x), and the number with the digits
reversed can be written as 10(15
x)þx. Since the new number is 9 more
than the original number, an equation can be written as

new number¼original numberþ 9

10(15
x)þx¼ 10 xþ(15
x)þ 9

IMPLEMENTATION: Solve the equation:

10 ð 15 
xÞþx¼ 10 xþð 15 
xÞþ 9

150 
 10 xþx¼ 10 xþ 15 
xþ 9

150 
 9 x¼ 9 xþ 24

150 
 9 x
 9 x¼ 9 x
 9 xþ 24

150 
 18 x¼ 24

150 
 150 
 18 x¼ 24 
 150

 18 x¼
 126

 181 x


 181

¼

126

18

x¼ 7

The ten’s digit is 7 and the one’s digit is (15
7)¼8. The number, then,

is 78.

LESSON 10 Solving Digit Problems 99