After selling half their card collections, DeShawn and Stephanie each buy 9 new cards. What is the ratio of the number of cards DeShawn has to the number Stephanie has?

Answer 1

Let $x$ be the original number of cards each person had. After selling half their collections, DeShawn and Stephanie each have $x/2$ cards. After buying new cards, they each have $(x/2)+9$ cards. The ratio of the number of cards DeShawn has to the number Stephanie has is $(x/2+9)/(x/2+9)=\boxed{1}$.