1985 AJHSME Problems/Problem 23

Problem

King Middle School has $600$ 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

If each student has $5$ classes, and there are $600$ students, then they have a total of $5\times 1200=6000$ classes among them.

Each class has $30$ students, so there must be $\frac{6000}{30}=200$ classes. Each class has $1$ teacher, so the teachers have a total of $200$ classes among them.

Each teacher teaches $4$ classes, so if there are $t$ teachers, they have $4t$ classes among them. This was found to be $200$ , so $4t=200\Rightarrow t=50$

This is answer choice $\boxed{\text{E}}$

Solution 2 (Similar to above solution)

Each teacher teaches $4$ classes and each class has $30$ students, so each teacher teaches $120$ students in one class.

So, to teach five classes, there has to be $5$ teachers, but there is $1200$ students, so multiply by $\frac{1200}{120}$ which is $50$ , or $\boxed{\textbf{(E)}\ 50}$

1985 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 22	Followed by Problem 24
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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1985 AJHSME Problems/Problem 23

Contents

Problem

Solution

Solution 2 (Similar to above solution)

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