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2008 AMC 10B Problem 4

Problem 4 of 25EasierAlgebraProblem-Solving Techniques

A semipro baseball league has teams with 2121 players each. League rules state that a player must be paid at least $15,000,\$15{,}000, and that the total of all players’ salaries for each team cannot exceed $700,000.\$700{,}000. What is the maximum possible salary, in dollars, for a single player?

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Solution

One player’s salary is largest when the other 2020 players each earn the minimum $15,000.\$15{,}000. That leaves $700,000−20⋅$15,000\$700{,}000-20\cdot\$15{,}000 =$700,000−$300,000=\$700{,}000-\$300{,}000 =$400,000=\$400{,}000 for the single player. Thus, the correct answer is C.
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Tagged: inequality · optimization · extremal argument

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