2460.28 – Present and Future Ages I

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:

(S+5)+(B+5)=34,S+B+10=34,S+B=24. \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=3BS = 3 B. Therefore we can write:

3B+B=24,4B=24,B=6. \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=34.11 + 23 = 34.