math !!!! :O
posted by Katherine 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?

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