# The sum of Buddy and Sol's age is 31. Ten years ago Sol's age was twice that of Buddy. Calculate their ages?

## (Question Restore: portions of this question have been edited or deleted!)

Jan 24, 2018

Buddy is 17 years old. Sol is 24 years old.

#### Explanation:

Equations
$B + S = 41$
$2 \left(B - 10\right) = S - 10$

Solution
$S = 2 \left(B - 10\right) + 10$
$S = 2 B - 10$
$B + 2 B - 10 = 41$
$3 B = 51$
$B = 17$
$S + 17 = 41$
$S = 24$

Jan 24, 2018

Buddy is $17$ and Sol is $24$

#### Explanation:

If we denote Buddy's current age by $B$, ans Sol's age by $S$ then:

The first line tells us that:

$B + S = 41$

Ten years ago, Buddy's age would have been $B - 10$ and Sol's age would have been $S - 10$, so the second line tells us that:

$\left(S - 10\right) = 2 \left(B - 10\right)$
$\therefore S - 10 = 2 B - 20$
$\therefore 2 B - S = 10$

We now need to solve the two equations simultaneously. If we add the two equations:

$3 B = 51 \implies B = 17$

And substituting this into the first equation:

$17 + S = 41 \implies S = 24$

Hence:

$B = 17$ and $S = 24$

Validation

$B + S = 17 + 24 = 41$
$B - 10 = 7$ and $S - 10 = 14$

Which satisfies the given conditions