Posted by **kaykay** on Thursday, April 7, 2011 at 4:40pm.

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 -
**Henry**, Saturday, April 9, 2011 at 10:17pm
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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