Question

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?

$270{,}000$

$385{,}000$

$400{,}000$

$430{,}000$

$700{,}000$

Answer: C

Concepts:optimization extremal argument

Difficulty rating: 1100

Solution:

One player earns the most when the other $20$ players each receive the minimum salary of $\$15{,}000.$

Thus the maximum salary is $\$700{,}000$ $- 20 \cdot \$15{,}000$ $= \$700{,}000$ $- \$300{,}000$ $= \$400{,}000.$

Thus, the correct answer is C.

2008 AMC 12B Problem 3

Answer: C

Difficulty rating: 1100

Solution:

Problem 3 in Other Years