SOLUTION: Several of us at work have attempted this with no success! A father and son are aged 71 and 34 respectively, at what age was the father 3 times the age of his son and at what age

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Question 550167: Several of us at work have attempted this with no success!
A father and son are aged 71 and 34 respectively, at what age was the father 3 times the age of his son and at what age will the son be half his fathers age?
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
Given in the problem:
f=71
s=34
Let's have x be the number of years ago. So if it was x=10 years ago the father would be 61 and the son 24
3(s-x)=(f-x)
Plug in the father and son's ages
3(34-x)=(71-x)
Distribute the 3
102-3x=71-x
+3x to both sides
102=71+2x
-71 to both sides
31=2x
x=15.5
15 and a half years ago the son was 18.5 and the father was 55.5 . 55.5 is 3 times 18.5. The fact that it doesn't turn out evenly makes the problem a bit harder to figure out.
For the other half we start with a similar equation. However, I'm going to use y and have it represent years from now because this hasn't happened yet.
(1/2)(71+y)=(34+y)
Multiply everything by 2 to clear the fractions
71+y=68+2y
71=68=y
3=y
So in 3 years the son will be 37 and dad will be 74.