1985 AMC 8 Problem 23

Attempt Problem 23 of the 1985 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1985 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

23.

King Middle School has 12001200 students. Each student takes 55 classes a day. Each teacher teaches 44 classes. Each class has 3030 students and 11 teacher. How many teachers are there at King Middle School?
3030
3232
4040
4545
5050
Answer: E
Concepts:double counting
Small hint:
Count the total number of student-class attendances: 1200×51200 \times 5
Big hint:
Divide by 3030 to get the number of classes, then by 44 to get the number of teachers
Solution:
Each day there are 1200×5=60001200 \times 5 = 6000 student-class attendances. Since each class holds 3030 students, there are 600030=200\dfrac{6000}{30} = 200 classes.
Each teacher teaches 44 classes, so there are 2004=50\dfrac{200}{4} = 50 teachers.
Thus, the correct answer is E .
LIVE by Po-Shen Loh
Programs

LIVE Classes

Self-Paced Classes

Stars

Scholarship

About Us

Who Is Po-Shen Loh?

Email Contact

Newsletter

Jobs

Become a Star

For a more Thought Full world.

© 2026 Expii, Inc.