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math

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The ratio of the number of postcards john had to the number of postcards Zachary ha d was 4:9. Zachary had 45 more postcards than John. After giving some postcards to John, Zachary had 6/7 as many postcards as John.

(A) How many postcards did Zachary have in the beginning?

(B) How many postcards did Zachary give to John?

Is there a way to figure this out without using formulas?

  • math - ,

    A. John has X cards.
    Zack has (X+45) cards.

    X/(X+45) = 4/9,
    Cross multiply:
    4x+180 = 9x,
    4x-9x = -180,
    -5x = -180,
    X = 36cards.
    X+45 = 36+45 = 81 cards.

    B. Zack has (81-X) cards.
    John has (36+X) cards.

    81-X = 6/7(36+X),
    Multiply both sides by 7:
    567-7X = 6(36+X),
    567-7X = 216+6X,
    -7X-6X = 216-567,
    -13X = -351,
    X = 27 cards given to John.

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