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?
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Set up a system of linear equations:
\[A + 10 = 2B\]
\[A -5 = 3B\]
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.
A + 10 = 2 X (B+10)
A - 5 = 3 X (B-5)
A = 50
B = 20