1985 AJHSME Problems/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

If each student has $5$ classes, and there are $1200$ 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 $1$ teachers, 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 $\boxed{\text{E}}$

See Also

1985 AJHSME (ProblemsAnswer KeyResources)
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
All AJHSME/AMC 8 Problems and Solutions


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