Question

The sum of the ages of the father and his son is 42 years. The product of their ages is 185. Find the age of the father and the son

Answer 1

Let f and s be the ages of the father and the son. We have

`\begin{cases}f+s=42\\fs=185\end{cases}`

From the first equation we derive

`f=42-s`

Substitute this expression for f in the second equation and we have

`(42-s)s=185 \iff -s^2+42s-185=0 \iff s^2-42s+185=0`

The solutions to this equation are s=5 or s=37

Since the sum of the ages must be 42, the solutions would imply

`s=5 \implies f=37,\quad s=37\implies f=5`

We can only accept the first solution, since the second would imply a son older than his father!