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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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