Math Word Problems Demystified - A Self Teaching Guide

EVALUATION: In 24 years, the daughter’s age is 3þ 24 ¼27 and the
mother’s age is 30þ 24 ¼54. Since 54¼ 2 27, the mother will be twice as
old as the daughter.

EXAMPLE:Bill is 8 years older than his brother. In 3 years, Bill will be twice
as old as his brother. Find their present ages.

SOLUTION:

GOAL: You are being asked to find the present ages of Bill and his brother.

STRATEGY: Letx¼Bill’s brother’s age andxþ 8 ¼Bill’s age. In 3 years,
their ages will bexþ 3 ¼Bill’s brother’s age and (xþ8)þ 3 ¼Bill’s age.
Now in 3 years, Bill will be twice as old. This means the equation is 2 times
Bill’s brother’s age in 3 years¼Bill’s age in 3 years or 2(xþ3)¼(xþ8)þ3.

IMPLEMENTATION: Solve the equation:

2 ðxþ 3 Þ¼ðxþ 8 Þþ 3

2 xþ 6 ¼xþ 8 þ 3

2 xþ 6 ¼xþ 11

2 x
xþ 6 ¼x
xþ 11

xþ 6 ¼ 11

xþ 6 
 6 ¼ 11 
 6

x¼ 5 ðBill’s brother’s ageÞ

xþ 8 ¼ 5 þ 8 ¼ 13 ðBill’s ageÞ

EVALUATION: In 3 years, Bill’s brother will be 5þ 3 ¼8 years, and Bill
will be 13þ 3 ¼16, which is twice his brother’s age.

EXAMPLE:Jan is 6 years older than Mary. If the sum of their ages is 32,
find each one’s age.

SOLUTION:

GOAL: You are being asked to find the ages of Jan and Mary.

LESSON 12 Solving Age Problems 123