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14 August, 02:54

If Abby gives $10 to Ben, then they will have the same amount of money. If Ben gives $20 to Abby, then she'll have four times as much as he has. How much money does each of them have now?

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  1. 14 August, 03:23
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    Abby has $60 and Ben has $40.

    Step-by-step explanation:

    Let a = Abby's money and b = Ben's money.

    We have two conditions:

    (1) a - 10 = b + 10

    (2) a + 20 = 4 (b - 20)

    Add 10 to each side of (1) (3) a = b + 20

    Distribute the 4 In (2) : a + 20 = 4b - 80

    Subtract 20 from each side: (4) a = 4b - 100

    Subtract (3) from (4) : 0 = 3b - 120

    Add 120 to each side: 120 = 3b

    Divide each side by 3: (5) b = 40

    Substitute (5) into (1) : a - 10 = 40 + 10

    a - 10 = 50

    Add 10 to each side: a = 60

    Abby has $60 and Ben has $40.

    Check:

    (1) 60 - 10 = 40 + 10 (2) 60 + 20 = 4 (40 - 20)

    50 = 50 80 = 4 * 20

    80 = 80
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