Math Word Problems Demystified - A Self Teaching Guide

The answers are
15 and
17, and 15 and 17.

4. Letx¼the smaller number
   andxþ 3 ¼the larger number

x^2 ¼ 3 ðxþ 3 Þþ 19

x^2 ¼ 3 xþ 9 þ 19

x^2 ¼ 3 xþ 28

x^2 
 3 x
 28 ¼ 3 x
 3 xþ 28 
 28

x^2 
 3 x
 28 ¼ 0

ðx
 7 Þðxþ 4 Þ¼ 0

x
 7 ¼ 0 xþ 4 ¼ 0

x
 7 þ 7 ¼ 0 þ 7 xþ 4 
 4 ¼ 0 
 4

x¼ 7 x¼
 4

xþ 3 ¼ 7 þ 3 ¼ 10 xþ 3 ¼
 4 þ 3 ¼
 1

The answers are 7 and 10, and
4 and
1.

5. Letx¼the time it takes the larger pipe to fill the tank
   andxþ 32 ¼the time it takes the smaller pipe to fill the tank; then

30

x

þ

30

xþ 32

¼ 1

the L.C.D.¼xðxþ 32 Þ

xðxþ 32 Þ

30

x

þxðxþ 32 Þ^1 

30

ðxþ 32 Þ^1

¼xðxþ 32 Þ

30 ðxþ 32 Þþ 30 x¼xðxþ 32 Þ

30 xþ 960 þ 30 x¼x^2 þ 32 x

238 LESSON 19 Using Quadratic Equations