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?

3 answers

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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