Question

有 $20$ 名学生参加课后项目，该项目提供瑜伽、桥牌和绘画课程。每名学生至少选一门课，也可以选两门或三门。

有 $10$ 人选瑜伽， $13$ 人选桥牌， $9$ 人选绘画。有 $9$ 人至少选了两门课。选了三门课的学生有多少人？

There are $20$ students participating in an after-school program offering classes in yoga, bridge, and painting. Each student must take at least one of these three classes, but may take two or all three.

There are $10$ students taking yoga, $13$ taking bridge, and $9$ taking painting. There are $9$ students taking at least two classes. How many students are taking all three classes?

$1$

$2$

$3$

$4$

$5$

答案：C

知识点：容斥原理方程组

难度评级：1280

解答：

总选课人次为 $10+13+9=32$ 。

设 $x$ 表示选 $1$ 门课的人数， $y$ 表示选 $2$ 门课的人数， $z$ 表示选 $3$ 门课的人数。

于是 $x+2y+3z = 32$ 。

因此总人数为 $20$ ，所以 $x+y+z = 20$ ，从而 $y+2z=12$ 。

至少选两门课的人数为 $9$ ，所以 $y+z = 9$ 。

因此 $z=3$ ，这就是答案。

所以正确答案是 C。

The number of classes taken total is $10+13+9=32.$

Let $x$ represent the number of people who take $1,$ let $y$ represent the number of people who take $2$ classes, and let $z$ represent the number of people who take $3$ classes.

Then, we know $x+2y+3z = 32.$

As such, the total number of people is $20,$ so $x+y+z = 20.$ This makes $y+2z=12.$

The number of people who take at least two classes is $9,$ so $y+z = 9.$

Therefore, $z=3,$ making that the answer.

Thus, the correct answer is C .

2017 AMC 10B 第 13 题

答案：C

难度评级：1280

解答：

其他年份的第 13 题