SOLUTION: Five years ago a man was five times as old as his son.ln 12 years time,the sum of their ages will be 84.Find their present ages.

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Question 1209543: Five years ago a man was five times as old as his son.ln 12 years time,the sum of their ages will be 84.Find their present ages.
Found 3 solutions by timofer, josgarithmetic, ikleyn:
Answer by timofer(104) About Me  (Show Source):
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m for the man and s for his son

m-5=5%28s-5%29 and m%2B12%2Bs%2B12=84

Some steps
m-5=5s-25 and m%2Bs=60
m=5s-20
and then
5s-20%2Bs=60
6s=80
3s=40
s=40%2F3 not a whole number

You want to recheck the original problem.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, the son's age
y, the father's age

Five years ago a man was five times as old as his son.ln 12 years time,the sum of their ages will be 84.
Find their present ages.
----------
d years ago a man was k times as old as his son. ln p years time,the sum of their ages will be T.
Find their present ages.
-----------

y-d=k%28x-d%29
and
%28x%2Bp%29%2B%28y%2Bp%29=T

y=kx-kd%2Bd
and x%2By=T-2p
and if substitute, then
x%2Bkx-kd%2Bd=T-2p
x%2Bkx=T-2p%2Bkd-d
x%281%2Bk%29=T-2p%2Bkd-d
highlight%28x=%28T-2p%2Bkd-d%29%2F%28k%2B1%29%29, just in general for the son's present age. But does this need
to be a positive whole number?

In the example given,
x=%2884-2%2A12%2B5%2A5-5%29%2F%285%2B1%29
x=%2860%2B20%29%2F6
x=80%2F6
x=40%2F3
x=13%261%2F3, the son's age. If to the nearest month is acceptable, then this should be fine.

If all that is fine then y=kx-kd%2Bd
y=5%2A%2813%261%2F3%29-5%2A5%2B5
y=5%2813%261%2F3%29-20
y=46%262%2F3

In case you can not accept non-whole number values, then something is wrong in the exercise description.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

In 12 years time, the sum of their ages will be 84 ---->

    Hence, right now the sum of their ages is  84 - 12 - 12 = 84 - 24 = 60 years



Right now the sum of their ages is 60 years  --->

    Hence, five years ago, the sum of their ages was  60 - 5 - 5 = 50.


So, according to the problem, five years ago, the father was five times as old 
as the son and the sum of their ages was 50.


But there are no such integer number that satisfy this condition - so the problem is DEFECTIVE.


                    A  CONCLUSION  and the  DIAGNOSIS:

        as presented in the post,  the problem is  FATALLY  DEFECTIVE.