Math Word Problems Demystified - A Self Teaching Guide

Likewise, if the problem gives you some information about the ages, say,

5 years ago, you can represent their past ages as

Letx
 5 ¼the daughter’s past age and

3 x
 5 ¼the mother’s past age

The basic strategy for solving age problems is to represent the present ages

of the people, represent the past or future ages of the people, and then set up

the equation.

EXAMPLE:A mother is ten times as old as her daughter; in 24 years, she will

be twice as old as her daughter. Find their present ages.

SOLUTION:

GOAL: You are being asked to find the present ages of the mother and

daughter.

STRATEGY: Letx¼the daughter’s present age and 10x¼the mother’s

present age. In 24 years, their ages will bexþ 24 ¼the daughter’s age and

10 xþ 24 ¼ the mother’s age. If the mother will be twice as old as her

daughter in 24 years, the equation is 2 times the daughter’s age in 24 years¼

the mother’s age in 24 years or 2(xþ24)¼ 10 xþ24.

IMPLEMENTATION: Solve the equation:

2 ðxþ 24 Þ¼ 10 xþ 24

2 xþ 48 ¼ 10 xþ 24

2 x
 10 xþ 48 ¼ 10 x
 10 xþ 24

 8 xþ 48 ¼ 24

 8 xþ 48 
 48 ¼ 24 
 48

 8 x¼
 24

 81 x


 81

¼

24

8

x¼3 (daughter’s age)

10 x¼ 10  3 ¼30 (mother’s age)

122 LESSON 12 Solving Age Problems