SOLUTION: at present,the sum of the ages of a father and his son is 43 years.In n years,n>0, the father will be four times the son age. Determine the possible age of the father and son?

Question 674014: at present,the sum of the ages of a father and his son is 43 years.In n years,n>0, the father will be four times the son age. Determine the possible age of the father and son?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
at present,the sum of the ages of a father and his son is 43 years.
f + s = 43
or
f = (43-s)
:
we have three unknowns and only two equations here, but full steam ahead!
:
In n years,n>0, the father will be four times the son age.
f + n = 4(s + n)
f + n = 4s + 4n
f = 4s + 4n - n
f = 4s + 3n
Replace f with (43-s)
43 - s = 4s + 3n
43 = 4s + s + 3n
43 = 5s + 3n
rearrange this
-5s = 3n - 43
mult by -1
5s = -3n + 43
Here is a break, since we are dealing with integers, we can say
"What value for n would make the value on the right a multiple of 5?"
How about n = 1
5s = -3(1) + 43
5s = 40
s = 40/5
s = 8 yrs old is the son's age
then Dad is 35 yrs old, right
:
In 1 yr, s=9: f=36, Dad is 4 times as old as sonny
:
:
But that is not the only solution, why don't you check it out when n = 6?
:
And how about when n=11?
:

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