2008 AMC 12B Problem 3

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 make one salary as large as possible, pay the other

20

players the minimum allowed

The maximum is

\$700{,}000

minus the total of

20

minimum salaries

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.

Problem 3 in other years