10 years from now A will be twice as old as B. Five years ago, A was three times as old as B. What are the present ages of A & B?

Question

anonymous · Answer

Set up a system of linear equations: 
$$A + 10 = 2B$$
$$A -5 = 3B$$

anonymous · Answer

One easy way to do that would be to multiply the top equation by 3, then multiply the bottom equation by 2 so that the left sides of both equations are equal to 6B. Then you can set them equal to each other and solve for either A or B to get one of the ages. Then take that value and substitute it back into either equation for solve for the other person's age.

anonymous · Answer

A + 10 = 2 X (B+10)
A - 5 = 3 X (B-5)
A = 50 
B = 20

anonymous · Answer

Ooh, good catch! I spaced the adjusting B's age too.