AMC12 2015 B

AMC12 2015 B · Q5

AMC12 2015 B · Q5. It mainly tests Linear inequalities, Ratios & proportions.

The Tigers beat the Sharks 2 out of the first 3 times they played. They then played N more times, and the Sharks ended up winning at least 95% of all the games played. What is the minimum possible value for N ?

Tigers在头三次比赛中2胜Sharks。然后又进行了N场比赛，Sharks最终赢得了所有比赛的至少95%。N的最小可能值为多少？

(A) 35 35

(B) 37 37

(D) 41 41

(E) 43 43

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): If the Sharks win the next $N$ games, then they win $\frac{1+N}{3+N}\cdot 100\%$ of the games. Therefore $\frac{1+N}{3+N}\ge \frac{95}{100}=\frac{19}{20}$, so $20+20N\ge 57+19N$. Therefore $N\ge 37$.

答案（B）：如果 Sharks 在接下来的 $N$ 场比赛中都获胜，那么他们赢下的比赛占总比赛的百分比为 $\frac{1+N}{3+N}\cdot 100\%$。因此 $\frac{1+N}{3+N}\ge \frac{95}{100}=\frac{19}{20}$，所以 $20+20N\ge 57+19N$。因此 $N\ge 37$。

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