Question

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!)

Answer 1

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

Explanation:

Equations
`B+S = 41`
`2(B-10)=S-10`

Solution
`S=2(B-10)+10`
`S=2B-10`
`B+2B-10=41`
`3B=51`
`B=17`
`S+17=41`
`S=24`

Answer 2

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:

`(S-10) = 2(B-10)`
`:. S-10 = 2B-20`
`:. 2B-S = 10`

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

`3B = 51 => B=17`

And substituting this into the first equation:

`17+S=41 => 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