AMC12 2008 B

AMC12 2008 B · Q3

AMC12 2008 B · Q3. It mainly tests Arithmetic misc, Optimization (basic).

A semipro baseball league has teams with $21$ players each. League rules state that a player must be paid at least $15,000$ dollars, and that the total of all players' salaries for each team cannot exceed $700,000$ dollars. What is the maximum possiblle salary, in dollars, for a single player?

一个半职业棒球联盟的每支球队有 $21$ 名球员。联盟规则规定，每名球员的薪水至少为 $15,000$ 美元，并且每支球队所有球员薪水总和不得超过 $700,000$ 美元。单个球员的最大可能薪水（美元）是多少？

(A) 270000 270000

(B) 385000 385000

(D) 430000 430000

(E) 700000 700000

Answer

Correct choice: (C)

正确答案：（C）

Solution

We want to find the maximum any player could make, so assume that everyone else makes the minimum possible and that the combined salaries total the maximum of $700,000$ $700,000 = 20 * 15,000 + x$ $x = 400,000$ The maximum any player could make is $400,000$ dollars $\Rightarrow C$

我们要使某一名球员的薪水最大，因此假设其他所有球员都拿最低薪水，并且球队总薪水达到上限 $700,000$ $700,000 = 20 * 15,000 + x$ $x = 400,000$ 因此单个球员的最大可能薪水为 $400,000$ 美元 $\Rightarrow C$。

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