If Frank and Sam total their ages the answer is 49 Frank is twice as old as Sam was when Frank was as old as Sam is now How old are Frank and Sam?

Answer 1

Frank is 28 and Sam is 21

When Frank was 21, Sam was 14. (see below for the algebra)

If you add Frank's age and Sam's age their ages will equal 49, there are only so many combinations that this can happen, through guess and checking I found that the answer is that Sam is now 21 years old and that Frank is now 28 years old. The wording of this makes it confusing and it might help to write down the thought behind it. Frank is twice as old as Sam was when Frank was as old as Sam is now. Frank was as old as Sam is now, 21 years old, that was 7 years ago. If Sam is 21 right now, then 7 years ago he was only 14 years old. Frank's current age is 28, which is twice as old as Sam was, 14 years old, when Frank was as old as Sam is now, 21 years old.

Current Frank+Current Sam= 49 28+21=49

Current Frank=Past Sam x2 28=14x2

Current Sam=Past Frank 21=21

The actual math

The actual algebraic solution is to set the time when the comparison is set as "t" years ago, where t = F - S

F = 2 (S - t) substitute F - S for t

F = 2S - 2F + 2S

3F = 4S

F = 4/3 S

and since F + S = 49

4/3 S + S = 49

7/3 S = 49

S = 21 and F = 28