math
posted by kaykay on .
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?

A. John has X cards.
Zack has (X+45) cards.
X/(X+45) = 4/9,
Cross multiply:
4x+180 = 9x,
4x9x = 180,
5x = 180,
X = 36cards.
X+45 = 36+45 = 81 cards.
B. Zack has (81X) cards.
John has (36+X) cards.
81X = 6/7(36+X),
Multiply both sides by 7:
5677X = 6(36+X),
5677X = 216+6X,
7X6X = 216567,
13X = 351,
X = 27 cards given to John.