SOLUTION: please help me solve a woman is 3 times as old as her son. 8 years ago the product of their ages was 112. find their present ages

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Question 1183200: please help me solve
a woman is 3 times as old as her son. 8 years ago the product of their ages was 112. find their present ages
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The problem can be solved very quickly informally....

When the product of their ages was 112, their possible ages were
112 and 1
56 and 2
28 and 4
14 and 8

The only logical choice is 28 and 4. That would make their current ages 36 and 12; and 36 is 3 times 12.

ANSWER: 36 and 12

Using formal algebra....

Let x be the son's age
Then 3x is the mother's age

Their ages 8 years ago were x-8 and 3x-8.

8 years ago the product of their ages was 112:
%283x-8%29%28x-8%29=112
3x%5E2-32x%2B64=112
3x%5E2-32x-48=0
%28x-12%29%283x%2B4%29=0
x=12 or x=-4%2F3

Obviously the negative fraction answer makes no sense.

ANSWERS:
The son's age is x=12
The mother's age is 3x=36