Write a system of equations to model each situation. Solve using any method: 10 years from now A 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?

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a=50 b=20

Step-by-step 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

70

step-by-step explanation: