Algebra
WORD PROBLEMS
Example 4:
A man is 21 years older than his son. Five years ago he was four times as old as his son.
How old is each now?
Solution:
Step 1.
Let x = Son’s Age Now
Step 2.
Then,
x + 21 = Father’s Age Now
x - 5 = Son’s Age Five Years Ago
(x + 21) - 5 = Father’s Age Five Years Ago
Step 3.
Five years ago the father was four times as old as his son.
(x + 21) - 5 = 4(x - 5)
Step 4.
(x + 21) - 5 = 4(x - 5)
x + 16 = 4x - 20
x - 4x = -20 - 16
-3x = -36
x = 12 years
Solving for the other unknowns:
x + 21 = 12 + 21
x + 21 = 33 years
Answers:
Son’s Age Now = 12 years
Father’s Age Now = 33 years
Step 5.
The man is 21 years older than his son.
12 + 21 = 33 years
Five years ago he was four times as old as his son.
33 - 5 = 28 = 4(12 - 5) = 4 x 7
Thus, the answers check.
Rev. 0
Page 49
MA-02
