Making Venn diagrams

Each child in a school plays soccer, tennis, or both. 1/7 of the soccer players also play tennis, and 1/9 of the tennis players also play soccer. Do more than 1/2 the children play tennis?

Let n denote the number of children who play both soccer and tennis. Then seven times as many, 7n, play soccer, and nine times as many, 9n, play tennis. But n play both soccer and tennis. Thus, 6n play soccer exclusively, and 8n play tennis exclusively. Therefore, there are 6n + n + 8n = 15n children in total. The proportion of tennis players to children is 9n/15n = 3/5, which is greater than 1/2.

Source: The Inquisitive Problem Solver