AMC 8 2025 Problem 17
AMC8 2025 年第 17 题
比与比例★★★☆☆
In the land of Markovia, there are three cities: , , and . There are 100 people who live in , 120 who live in , and 160 who live in . 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, of the people who live in work in .) How many people work in ?
马克维亚大陆有三座城市：A城、B城和C城。A城有100人居住，B城有120人居住，C城有160人居住。每个人都在A城、B城或C城中的一个城市工作，且有的人可能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上，标注了居住在第一座城市的人群中，在第二座城市工作的比例。（例如，居住在A城的人中，有1/4在B城工作。）请问有多少人在A城工作？
- A.55
- B.60
- C.85
- D.115
- E.160
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
There are people who do not work in city that live in city , meaning that 100 - 45 = 55 people who live in city work in city . There are people who live in city and work in , as well as people who live in city that work in city . Therefore, the answer is 55 + 40 + 20 = 115.
We could also make an equation. Let's denote the number of people that live in city as , as , and as . If denotes the number of people working in city , then . This is because of the people from City and of the people from City work in city as shown in the image. We also know that of the people living in work in other cities. We are already given the values of variables , , and as 100, 120, and 160 respectively. Plug the values it into the main equation like this: . We solve for it and get our answer 115.
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