let the number of Patricia's card be x
then Anna's card will be = 3/4x
Half of Anna's card = 3/4x X 1/2
= 3/8x
Half give to Patricia = x + 3/8x
= 8x + 3x/8
= 11/8x
therefore, the ratio of Anna to Patricia is:
= 3/8x : 11/8x
= 3 : 11
so, the ratio of Anna's cards to Patricia's cards is 3 : 11