1985 AJHSME Problem 23

Problem

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?

$\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 45 \qquad \text{(E)}\ 50$

Solution

The students take a total of $1200 \cdot 5 = 6000$ classes, which requires $\frac{6000}{30 \cdot 4} = \boxed{50}$ teachers. The answer is E.

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1985 AJHSME Problem 23

Problem

Solution