AMC10 2008 B

AMC10 2008 B · Q4

AMC10 2008 B · Q4. 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, 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?

一个半职业棒球联盟的每个队有21名球员。联盟规则规定，每名球员的薪水至少为15000美元，每队的球员总薪水不得超过700000美元。一名球员的最大可能薪水是多少美元？

(A) 270,000 270000

(B) 385,000 385000

(D) 430,000 430000

(E) 700,000 700000

Answer

Correct choice: (C)

正确答案：（C）

Solution

A single player can receive the largest possible salary only when the other 20 players on the team are each receiving the minimum salary of $15,000$. Thus the maximum salary for any player is $700,000 - 20 \cdot 15,000 = 400,000$.

一名球员只能在队上其他20名球员每人都拿到最低薪水15000美元时获得最大可能薪水。因此，任何球员的最大薪水是 $700,000 - 20 \cdot 15,000 = 400,000$。

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