2008 AMC 10B Problems/Problem 4

Problem

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

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

Solution

The maximum occurs when 20 players get the minimum wage and the total of all players' salaries is 700000. That is when one player gets $700000-15000*20=400000\Rightarrow \boxed{\mathrm{(C)}}$ .

2008 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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2008 AMC 10B Problems/Problem 4

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