Math Word Problems Demystified - A Self Teaching Guide

SOLUTION:

GOAL: You are being asked to find two numbers whose sum is 12 and whose

reciprocal sum is^38 :

STRATEGY: Letx¼one number

and 12
x¼the other number

The reciprocals are

1

x

and

1

12 
x

:

Then the sum of the reciprocals is

1

x

þ

1

12 
x

¼

3

8

:

IMPLEMENTATION: Solve the equation:

1

x

þ

1

12 
x

¼

3

8

L:C:D:¼ 8 xð 12 
xÞ

8 xð 12 
xÞ

1

x

þ 8 xð 12 
xÞ^1 

1

ð 12 
xÞ^1

¼ 81 xð 12 
xÞ

3

81

8 ð 12 
xÞþ 8 x¼ 3 xð 12 
xÞ

96 
 8 xþ 8 x¼ 36 x
 3 x^2

96 ¼ 36 x
 3 x^2

3 x^2 
 36 xþ 96 ¼ 36 x
 36 x
 3 x^2 þ 3 x^2

3 x^2 
 36 xþ 96 ¼ 0

Divide by 3: x^2 
 12 xþ 32 ¼ 0

ðx
 4 Þðx
 8 Þ¼ 0

x
 4 ¼ 0 x
 8 ¼ 0

x
 4 þ 4 ¼ 0 þ 4 x
 8 þ 8 ¼ 0 þ 8

x¼ 4 x¼ 8

LESSON 19 Using Quadratic Equations 235