# Math Help - Problem on ages

1. ## Problem on ages

Help required to solve my algebra 2 homework on ages

The sum of the ages of a father and his is 45 years. Five years ago , the product of their ages was 34. What are the ages of the father and son?

2. ## Re: Problem on ages

Originally Posted by burgess
Help required to solve my algebra 2 homework on ages

The sum of the ages of a father and his is 45 years. Five years ago , the product of their ages was 34. What are the ages of the father and son?
let the age of father be $f$ and the age of the son be $s$

from the first line

$f+s=45$

from the second line

$(f-5)(s-5)=34$

and of course the father is older than the son, i.e.

$f>s$

you should be able to finish from here.

3. ## Re: Problem on ages

x - father's age
y - son's age

x+y=45
y=45-x
(x-5)(y-5)=34
xy-5y-5x+25=34
x(45-x)-5(45-x)-5x=9
45x-x2-225+5x-5x=9
-x2+45x-234=0

Solving this quadratic equation, x=39 and y=45-39=6

So, father is 39 years old and son is 6 years old.

4. ## Re: Problem on ages

Thank you all for the detail explanations