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 ag

Question

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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Kim Cúc 5 months 2021-08-18T01:33:01+00:00 1 Answers 5 views 0

Answers ( )

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    2021-08-18T01:34:07+00:00

    Answer:

    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

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