# When the son will be as old as his father today, the sum of their ages then will be 126. When the father was as old as his son is today, the sum of their ages was 38. Find their ages?

Mar 7, 2016

son's age : 30
father's age : 52

#### Explanation:

We shall represent the son's age 'today' by S and the father's age 'today' by F.

The first peace of information we have is that when the son's age(S+a few years) shall be equal to the father's present age(F), the sum of their ages shall be $126$.

we shall then note that S $+ x =$ F
where $x$ represent a number of years.

We now say that in $x$ years the father's age will be F $+ x$.

So the first information we have is : S $+ x +$ F $+ x = 126$
but S $+ x = F \rightarrow x =$ F-S
$\implies 3$F $- S = 126$ ......(1)

The second information is that when the father's age was equal to the son's present age(father = F - a few year = S), the sum of their ages was $38$.

we shall then note that F $- y =$ S
where $y$ represent a number of years.

This means that $y$ years earlier the father's age was F $- y$.

This information translated into math is : F $- y +$ S $- y = 38$
but F $- y =$ S $\rightarrow y =$ F-S
$\implies 3$ S-F $= 38$ ......(2)

Solve equation (1) and (2) to obtain
$\left\{\begin{matrix}F = 52 \\ S = 30\end{matrix}\right.$