2008 AMC 10B Problem 4

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

To maximize one salary, pay everyone else as little as allowed

The other

20

players each earn

\$15{,}000

One player’s salary is largest when the other

20

players each earn the minimum

\$15{,}000.

That leaves

\$700{,}000-20\cdot\$15{,}000

=\$700{,}000-\$300{,}000

=\$400{,}000

for the single player.

Thus, the correct answer is C.

Problem 4 in other years