Math Word Problems Demystified - A Self Teaching Guide

In this lesson, a sample of each type of problem is solved by using a system

of two equations with two unknowns. You will find the exact same problems

in the previous sections. This was done so that you can compare the two

methods (i.e., solving a problem using one equation versus solving a problem

using two equations). For some types of problems, such as lever and work

problems, it is better to use one equation.

EXAMPLE:One number is 8 more than another number and the sum of the

two numbers is 26. Find the numbers.

SOLUTION:

GOAL: You are being asked to find two numbers.

STRATEGY: Letx¼the smaller number

andy¼the larger number

Since one number is 8 more than the other number, the first equation is

y¼xþ 8

Since the sum of the two numbers is 26, the second equation is

xþy¼ 26

IMPLEMENTATION: Solve the system

y¼xþ 8

xþy¼ 26

Substitute the value foryin the second equation and solve forxsince

y¼xþ8.

xþy¼ 26

xþxþ 8 ¼ 26

2 xþ 8 ¼ 26

2 xþ 8 
 8 ¼ 26 
 8

208 LESSON 18 Using Two Equations