Question

在一次聚会上，每位男士正好与三位女士跳舞，每位女士正好与两位男士跳舞。共有十二位男士参加聚会。共有多少位女士参加？

At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the party. How many women attended the party?

$8$

$12$

$16$

$18$

$24$

答案：D

知识点：双重计数数对计数

难度评级：1190

解答：

从男士角度数，跳舞配对数为 $12 \cdot 3 = 36$ 。每位女士恰好在 $2$ 对中，所以女士人数为 $\dfrac{36}{2} = 18.$

所以正确答案是 D。

The number of dancing pairs is $12 \cdot 3 = 36,$ counting from the men's side. Each woman was in exactly $2$ pairs, so the number of women is $\dfrac{36}{2} = 18.$

Thus, the correct answer is D.

2004 AMC 10A 第 13 题

答案：D

难度评级：1190

解答：

其他年份的第 13 题