AMC 8 2013 Problem 16

AMC8 2013 年第 16 题

比与比例★★★☆☆

A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of

8^\text{th}

-graders to

6^\text{th}

-graders is

5:3

, and the the ratio of

8^\text{th}

-graders to

7^\text{th}

-graders is

8:5

. What is the smallest number of students that could be participating in the project?

Fibonacci 中学的一些学生正在参加一项社区服务项目。其中，八年级和六年级学生的个数之比为 5：3，八年级学生和七年级学生的个数之比是 8：5．那么参加这个项目的学生数最少是多少个？

A.16
B.40
C.55
D.79
E.89

正确答案 · Correct Answer

解析 · Solution

Solution 1

The number of 8 th 8 th -graders must be a multiple of both 5 5 and 8 8, so it must be at least 40 40. If there are 40 8 th 408 th -graders, then there are 3 5 ( 40 ) = 24 5 3 (40)=24 6 th 6 th -graders and 5 8 ( 40 ) = 25 7 th 8 5 (40)=257 th -graders, for a total of 40 + 24 + 25 = 89 40+24+25=89 students. Answer: 𝐸 E .

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