2460.28 – Present and Future Ages I

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: $11 + 23 = 34$.