SOLUTION: A father is twice a old as his son is today. A few years back, he was thrice as old and half that number of years prior to that, he was 5 times as old; and 6 years before that, he

Question 286065: A father is twice a old as his son is today. A few years back, he was thrice as old and half that number of years prior to that, he was 5 times as old; and 6 years before that, he was as old as his son is today. The father age is (in yrs)
Found 2 solutions by richwmiller, ptaylor:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
where is the money?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=son's age today
Then 2x=father's age today
t years back, we have:
x-t=son's age t years back
2x-t=father's age t years back and we are told:
2x-t=3(x-t)=
2x-t=3x-3t
x=2t-----------------------eq1
t/2 years before this we have:
x-t-t/2=x-3t/2=son's age half that number of years before that
2x-3t/2=father's age half that number of years before that and we are told:
2x-3t/2=5(x-3t/2)=
2x-3t/2=5x-15t/2 multiply each term by 2
4x-3t=10x-15t
12t=6x
or
x=2t or t=x/2 same as before----------------------eq2
6 years before this
x-(3t/2)-6=son's age
2x-(3t/2)-6=fathers age and we are told that:
2x-(3t/2)-6=x---------------eq3 multiply each term by 2
4x-3t-12=2x
2x-3t=12--------------eq3
substitute t=x/2 in eq3
2x-3(x/2)=12 multiply each term by 2
4x-3x=24
x=24---------son's age now
t=x/2=12 years
2x=2*24=48----father's age now
CK
12 years ago:
son was 24-12=12
father was 48-12=36 or 3*12
6 years prior to that:
son was 12-6=6
father36-6=30 or 5*6
6 years prior to that:
father was 30-6=24 same as son's age now

Hope this helps--ptaylor
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