2008 AMC 12B Problems/Problem 3

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?

$\textbf{(A)}\ 270,000 \qquad \textbf{(B)}\ 385,000 \qquad \textbf{(C)}\ 400,000 \qquad \textbf{(D)}\ 430,000 \qquad \textbf{(E)}\ 700,000$

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 (answer choice C)

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2008 AMC 12B Problems/Problem 3

Problem 3

Solution