Joe and Anna collect football cards.The greatest common factor of the numbers of cards in their collections is 15.Altogether Joe and Anna have 75 cards.If Joe has more cards than Anna,how many cards do they each have?

Answer 1

since 15 is a common factor the number of cards each has must be a multiple of 15

let the number of cards that Joe has be 15x, let Anna's number of cards be 15y

then 15x + 15y = 75
x + y = 5
also x > y , and of course both x and y must be whole numbers.

there are only 2 possibilities for x and y

(4,1), (3,2)

(4,1) : Joe has 60, Anna has 15
(3,2) : Joe has 45, Anna has 30

both cases satisfy your 3 conditions.