Adam and Claire each had a collection of postcards. Claire had 4/7 as many postcards as Adam. When Adam gave away 35 postcards, Claire then had twice as many as Adam. How many postcards were in Adam's collection at first?
cards originally had by adam = x, cards originally had by claire = y.
7/4 y = x from sentence 1
1/2y = x - 35(I'm assuming your questions means that Adam did not give the postcards away to claire here)
7/4y - x = 0
1/2y - x = -35
equation 1 - equation 2 to get
5/4y = 35
y = 28, and
x = 49
Adam originally had 49 cards, and Claire originally had 28 cards