AMC12 2008 12B, Problem 3

A semipro baseball league has teams with $21$ players each. League rules state that a player must be paid at least $15,000$ dollars, and that the total of all players' salaries for each team cannot exceed $700,000$ dollars. What is the maximum possiblle salary, in dollars, for a single player?

Solution: We want to find the maximum any player could make, so assume that everyone else makes the minimum possible and that the combined salaries total the maximum of $700,000$ $700,000 = 20 * 15,000 + x$ $x = 400,000$ The maximum any player could make is $400,000$ dollars $$ $\fbox{400,0}$.

Answer: 400,0