Question

Steph 在一场比赛上半场 $20$ 次出手进了 $15$ 球，下半场 $10$ 次出手进了 $10$ 球。Candace 上半场出手 $12$ 次，下半场出手 $18$ 次。在每个半场中，Steph 的命中率都高于 Candace。令人惊讶的是，她们最终总命中率相同。Candace 下半场比上半场多进了多少球？

Steph scored $15$ baskets out of $20$ attempts in the first half of a game, and $10$ baskets out of $10$ attempts in the second half. Candace took $12$ attempts in the first half and $18$ attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?

$7$

$8$

$9$

$10$

$11$

答案：C

知识点：百分数不等式

难度评级：1460

解答：

Steph 总共进了 $25$ 球，出手 $30$ 次。Candace 也出手了 $12+18=30$ 次，且两人的总命中率相同，所以 Candace 也进了 $25$ 球。

设 Candace 上半场进 $f$ 球，下半场进 $s$ 球，则 $f+s=25$ 。

Steph 上半场命中率为 $\frac{15}{20}=\frac34$ ，所以 $\frac{f}{12}<\frac34$ ，得到 $f<9$ 。Steph 下半场命中率为 $1$ ，所以 $s<18$ 。

因此 $f\le8$ 且 $s\le17$ 。又 $f+s=25$ ，唯一可能是 $f=8$ 、 $s=17$ ，所以 $s-f=9$ 。

正确答案是 C。

Steph made $25$ baskets in $30$ attempts. Candace also took $12+18=30$ attempts, and their overall percentages were the same, so Candace also made $25$ baskets.

Let $f$ be Candace's first-half baskets and $s$ be her second-half baskets. Then $f+s=25$ .

Steph's first-half percentage was $\frac{15}{20}=\frac34$ , so $\frac{f}{12}<\frac34$ , giving $f<9$ . Steph's second-half percentage was $1$ , so $s<18$ .

Thus $f\le8$ and $s\le17$ . Since $f+s=25$ , the only possibility is $f=8$ and $s=17$ , so $s-f=9$ .

Thus, the correct answer is C.

2022 AMC 8 第 21 题

答案：C

难度评级：1460

解答：

其他年份的第 21 题