## 2460.28 – Present and Future Ages II

Sosthenes is three times as old as Benoni. Five years from now, the sum of their ages will be thirty-four years. What are their present ages?

## Solution

In five years, Sosthenes and Benoni will have each gained five years for a total of thirty-four years between them. This means that the sum of their ages today is twenty-four years:

$\begin{aligned}
(S + 5) + (B + 5) &=& 34, \\
S + B + 10 &=& 34, \\
S + B &=& 24.
\end{aligned}$

In addition, Sosthenes is three times as old as Benoni, $S = 3 B$. Therefore we can write:

$\begin{aligned}
3 B + B &=& 24, \\
4 B &=& 24, \\
B &=& 6.
\end{aligned}$

As Benoni’s current age is six years, Sosthenes’s current age is eighteen years.

Check: $11 + 23 = 34.$