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:
\[A + 10 = 2B\]
\[A -5 = 3B\]

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

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