Question

Fibonacci Middle School 的一些学生参加社区服务项目。 $8$ 年级学生与 $6$ 年级学生的比为 $5:3$ ， $8$ 年级学生与 $7$ 年级学生的比为 $8:5$ 。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 $8$ th-graders to $6$ th-graders is $5:3,$ and the ratio of $8$ th-graders to $7$ th-graders is $8:5.$ What is the smallest number of students that could be participating in the project?

$16$

$40$

$55$

$79$

$89$

答案：E

知识点：比与比例最小公倍数

难度评级：1370

视频讲解：

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文字解答：

$8$ 年级学生人数必须同时是 $5$ 和 $8$ 的倍数，所以最少为 $40$ 这时 $6$ 年级人数为 $40 \cdot \dfrac{3}{5} = 24$ ， $7$ 年级人数为 $40 \cdot \dfrac{5}{8} = 25$ 。

因此学生总数为 $40 + 24 + 25 = 89$ 。

所以正确答案是 E。

The number of $8$ th-graders must be a multiple of $5$ and $8,$ which means that it is at least $40.$ Using this number, we get that the number of $6$ th-graders is $40 \cdot \dfrac{3}{5} = 24.$ Similarly, the number of $7$ th-graders is $40 \cdot \dfrac{5}{8} = 25.$

The total number of students is therefore $40 + 24 + 25 = 89.$

Thus, E is the correct answer.

2013 AMC 8 第 16 题

答案：E

难度评级：1370

视频讲解：

文字解答：

其他年份的第 16 题