AMC 8 1985 Problem 23

AMC8 1985 年第 23 题

比与比例★★★☆☆

King Middle School has 1200 students. Each student takes 5 classes a day. Each teacher teaches 4 classes. Each class has 30 students and 1 teacher. How many teachers are there at King Middle School?

King 中学有 1200 名学生。每名学生每天上 5 节课。每位教师每天教 4 节课。每节课有 30 名学生和 1 名教师。King 中学有多少名教师？

A.30
B.32
C.40
D.45
E.50

正确答案 · Correct Answer

解析 · Solution

Solution 1

Each of the 1200 students attends 5 class sessions, so they collectively attend a total of

1200 \cdot 5 = 6000

class sessions. Since 30 students attend each class session, there must be

\displaystyle \frac{6000}{30}=200

class sessions held. Since each class has 1 teacher, the teachers collectively host a total of

200 \cdot 1 = 200

class sessions. Since each teacher hosts 4 class sessions, there must be

\displaystyle \frac{200}{4} = 50

teachers.

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