Question

在 Markovia，有三座城市： $A$ 、 $B$ 、 $C$ 。住在 $A$ 的有 $100$ 人，住在 $B$ 的有 $120$ 人，住在 $C$ 的有 $160$ 人。每个人都在三座城市之一工作，也可以在自己居住的城市工作。下图中，从一座城市指向另一座城市的箭头标有居住在第一座城市且在第二座城市工作的人所占比例。（例如，住在 $A$ 的人中有 $\frac{1}{4}$ 在 $B$ 工作。）有多少人在 $A$ 工作？

In the land of Markovia, there are three cities: $A,$ $B,$ and $C.$ There are $100$ people who live in $A,$ $120$ who live in $B,$ and $160$ who live in $C.$ Everyone works in one of the three cities, and a person may work in the same city where they live. In the figure below, an arrow pointing from one city to another is labeled with the fraction of people living in the first city who work in the second city. (For example, $\frac{1}{4}$ of the people who live in $A$ work in $B.$ ) How many people work in $A?$

$55$

$60$

$85$

$115$

$160$

答案：D

知识点：分数

难度评级：1340

视频讲解：

Click to load, then click again to play

文字解答：

住在 $A$ 且在 $A$ 工作的人数为也就是住在 $B$ 且在 $A$ 工作的人数为住在 $C$ 且在 $A$ 工作的人数为所以答案为选 D。 $100 - 100 \times \frac{1}{4} - 100 \times \frac{1}{5}$ $100 - 25 - 20 = 55.$ $120 \times \frac{1}{3} = 40$ $160 \times \frac{1}{8} = 20$ $55 + 40 + 20 = 115,$

The number of people who live in $A$ and work in $A$ is $100 - 100 \times \frac{1}{4} - 100 \times \frac{1}{5}$ which is $100 - 25 - 20 = 55.$ The number of people who live in $B$ and work in $A$ is $120 \times \frac{1}{3} = 40$ The number of people who live in $C$ and work in $A$ is $160 \times \frac{1}{8} = 20$ So, the answer is $55 + 40 + 20 = 115,$ which is choice D.

2025 AMC 8 第 17 题

答案：D

难度评级：1340

视频讲解：

文字解答：

其他年份的第 17 题