SOLUTION: a boy's age is one third of his father's age. In ten years the son's age will be three less than half the father's age. Find the age of each. B= boys age F= fathers age I fou

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Question 907097: a boy's age is one third of his father's age. In ten years the son's age will be three less than half the father's age. Find the age of each.
B= boys age
F= fathers age
I found the variables to equal:
3b= f
B=1/3F
My equation was
10+b=1/2f-3

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +f+ = father's age now
Let +s+ = son's age now
+f+%2B+10+ = father's age in 10 yrs
+s+%2B+10+ = son's age in 10 yrs
--------------------------------
(1) +s+=+%281%2F3%29%2Af+
(2) +s+%2B+10+=+%281%2F2%29%2A%28+f+%2B+10+%29+-+3+
---------------------------------
(2) +2%2A%28+s+%2B+10+%29+=+f+%2B+10+-+6+
(2) +2s+%2B+20+=+f+%2B+4+
(2) +f+-+2s+=+16+
and
(1) +f+=+3s+
Substitute (1) into (2)
(2) +3s+-+2s+=+16+
(2) +s+=+16+
and
(1) +f+=+3%2A16+
(1) +f+=+48+
-----------------
The father is 48
The son is 16
---------------
check:
(2) +s+%2B+10+=+%281%2F2%29%2A%28+f+%2B+10+%29+-+3+
(2) +16+%2B+10+=+%281%2F2%29%2A%28+48+%2B+10+%29+-+3+
(2) +26+=+%281%2F2%29%2A58+-+3+
(2) +26+=+29+-+3+
(2) +26+=+26+
OK