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!)

2 Answers
Jan 24, 2018

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

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:

(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