AMC8 2013

AMC8 2013 · Q16

AMC8 2013 · Q16. It mainly tests Ratios & proportions.

A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of 8th-graders to 6th-graders is 5 : 3, and the ratio of 8th-graders to 7th-graders is 8 : 5. What is the smallest number of students that could be participating in the project?

斐波那契中学的多名学生参加了一个社区服务项目。八年级学生与六年级学生的比例是 5 : 3，八年级学生与七年级学生的比例是 8 : 5。参加该项目的最少学生人数是多少？

(A) 16 16

(B) 40 40

(D) 79 79

(E) 89 89

Answer

Correct choice: (E)

正确答案：（E）

Solution

We multiply the first ratio by 8 on both sides, and the second ratio by 5 to get the same number for 8th graders, in order that we can put the two ratios together: $5:3 = 5(8):3(8) = 40:24$ $8:5 = 8(5):5(5) = 40:25$ Therefore, the ratio of 8th graders to 7th graders to 6th graders is $40:25:24$. Since the ratio is in lowest terms, the smallest number of students participating in the project is $40+25+24 = \boxed{\textbf{(E)}\ 89}$.

我们将第一个比例两边乘以 8，第二个比例两边乘以 5，使八年级学生的数量相同，从而可以将两个比例合并： $5:3 = 5(8):3(8) = 40:24$ $8:5 = 8(5):5(5) = 40:25$ 因此，八年级：七年级：六年级的比例是 $40:25:24$。由于该比例已为最简形式，参加项目的最少学生人数是 $40+25+24 = \boxed{\textbf{(E)}\ 89}$。

Topics

AR.004 Ratios & proportions