5people enter a racquetball tournament in which each person must play evert other person exactly once. determine the total number of games that will be played

This is the "handshake problem", namely with n people, how many handshakes will there be if every will shake hands with everyone else.
n people will shake hands with (n-1) other people.  Since we are counting twice for each handshake, the number of handshakes is n(n-1)/2.
For n=5, the number of matches is 5(5-1)/2=10.
This is also the number of diagonals in an n-sided convex polygon.

Ithink you're supposed to multiply 12.50 which is how much he makes per hour and then multiply it by each number then add whats left togrther and there's your answer