Math Word Problems Demystified - A Self Teaching Guide

2. Letx¼one number

andxþ 6 ¼the other number

xðxþ 6 Þ¼ 91

x^2 þ 6 x¼ 91

x^2 þ 6 x
 91 ¼ 91 
 91

x^2 þ 6 x
 91 ¼ 0

ðxþ 13 Þðx
 7 Þ¼ 0

xþ 13 ¼ 0 x
 7 ¼ 0

xþ 13 
 13 ¼ 0 
 13 x
 7 þ 7 ¼ 0 þ 7

x¼
 13 x¼ 7

xþ 6 ¼
 13 þ 6 ¼
 7 xþ 6 ¼ 7 þ 6 ¼ 13

The answers are
7 and
13, and 7 and 13.

3. Letx¼one number

andxþ 2 ¼the other number

xðxþ 2 Þ¼ 255

x^2 þ 2 x¼ 255

x^2 þ 2 x
 255 ¼ 255 
 255

x^2 þ 2 x
 255 ¼ 0

ðxþ 17 Þðx
 15 Þ¼ 0

xþ 17 ¼ 0 x
 15 ¼ 0

xþ 17 
 17 ¼ 0 
 17 x
 15 þ 15 ¼ 0 þ 15

x¼
 17 x¼ 15

xþ 2 ¼
 17 þ 2 ¼
 15 xþ 2 ¼ 15 þ 2 ¼ 17

LESSON 19 Using Quadratic Equations 237