Math Word Problems Demystified - A Self Teaching Guide

meaningful. This will be shown in some problems. In that case, disregard the

solution that does not make sense. (Note:Sometimes the two solutions are

equal to each other; in that case there is only one solution.)

EXAMPLE:If the sum of two numbers is 20 and the product of the two

numbers is 36, find the numbers.

SOLUTION:

GOAL: You are being asked to find two numbers whose sum is 20 and whose

product is 36.

STRATEGY: Letx¼one number

and 20
x¼the other number

If the product of the two numbers is 36, the equation isx(20
x)¼36.

IMPLEMENTATION: Solve the equation:

xð 20 
xÞ¼ 36

20 x
x^2 ¼ 36

0 ¼x^2 
 20 xþ 36

0 ¼ðx
 18 Þðx
 2 Þ

x
 18 ¼ 0 x
 2 ¼ 0

x
 18 þ 18 ¼ 0 þ 18 x
 2 þ 2 ¼ 0 þ 2

x¼ 18 x¼ 2

Hence the two numbers are 18 and 2.

EVALUATION: Check the facts of the problem. The sum 18þ2 is 20 and

the product 18 2 ¼36.

EXAMPLE:If the product of two consecutive numbers is 306, find the

numbers.

LESSON 19 Using Quadratic Equations 233