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math !!!! :O

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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?

  • math !!!! :O - ,

    The way you define your variables is very crucial

    let the number of cards John has be 4x
    let the number of cards Zach has be 9x
    (notice 4x : 9x = 4:9 )

    Zach has 45 more than John
    so 9x = 4x + 45
    5x = 45
    x = 9

    so now we know that John has 36 and Zach has 81

    so after the "give-away"
    John has 36+y
    Zach has 81-y

    we are told that now Zach has 6/7 as many as John
    81-y = (6/7)(36+y)
    567 - 7y = 216 + 6y
    -13y = -351
    y = 27

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