10 years from now, a you will be twice as old as b. 5 years ago, a was three times as old as b. what are the present ages of a and b?

A = 50 and B = 20
Explanation:
Call A and B the 2 present ages.
Ten years from now, A is twice as old as B -->
(A + 10) = 2(B + 10) (1)
Five years ago, A was 3 times as old as B -->
(A - 5) = 3(B - 5) (2).
Solve the system (1) and (2).
From (2) --> A = 3B - 15 + 5 = 3B - 10.
Replace this value of A into (1) -->
3B - 10 + 10 = 2B + 20 --> B = 20. Then,
A = 3B - 10 = 60 - 10 = 50.
Check
!0 years from now --> A = 60 and B = 30 --> A = 2B .OK
5 years ago --> A = 45 and B = 15 --> A = 3B. OK

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