2013 AMC 8 第 16 题
先试着解答 2013 AMC 8 第 16 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2013 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
16.
斐波那契中学的一些学生参加社区服务项目。 年级学生与 年级学生的比为 ， 年级学生与 年级学生的比为 。参加该项目的学生最少可能有多少人？
A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of th-graders to th-graders is and the ratio of th-graders to th-graders is What is the smallest number of students that could be participating in the project?
小提示：
八年级学生人数必须同时适合两个比例
The number of eighth-graders must fit both ratios.
大提示：
使用 和 的最小公倍数
Use the least common multiple of and .
视频讲解：
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文字解答：
年级学生人数必须同时是 和 的倍数，所以最少为 。这时 年级人数为 ， 年级人数为 。
因此学生总数为 。
所以正确答案是 E。
The number of th-graders must be a multiple of and which means that it is at least Using this number, we get that the number of th-graders is Similarly, the number of th-graders is
The total number of students is therefore
Thus, E is the correct answer.
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