2008 AMC 12B 第 3 题

Question

一个半职业棒球联盟中每队有

21

名球员。联盟规则规定，每名球员工资至少为

\$15{,}000

，并且每队所有球员工资总和不能超过

\$700{,}000

。单名球员最高可能工资是多少美元？

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

要让一个人的工资尽可能大，就让其他

20

名球员都拿允许的最低工资。

To make one salary as large as possible, pay the other

20

players the minimum allowed

最大工资等于

\$700{,}000

减去

20

份最低工资的总和。

The maximum is

\$700{,}000

minus the total of

20

minimum salaries

当其他

20

名球员每人都拿最低工资

\$15{,}000

时，一名球员的工资最大。

因此最大工资为

\$700{,}000

- 20 \cdot \$15{,}000

= \$700{,}000

- \$300{,}000

= \$400{,}000

。

因此，正确答案是 C。

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.

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