1985 AJHSME Problems/Problem 23: Difference between revisions

Revision as of 21:33, 12 January 2009

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 $\boxed{\text{D}}$

Revision as of 21:33, 12 January 2009 view source 5849206328x (talk \| contribs) editor 1,190 edits New page: ==Problem== King Middle School has <math>1200</math> students. Each student takes <math>5</math> classes a day. Each teacher teaches <math>4</math> classes. Each class has <math>30</ma...		Revision as of 21:33, 12 January 2009 view source 5849206328x (talk \| contribs) editor 1,190 edits m →See Also Newer edit →
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	==See Also==		==See Also==

	[[1985 AJHSME]]		[[1985 AJHSME Problems]]

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1985 AJHSME Problems/Problem 23: Difference between revisions

Revision as of 21:33, 12 January 2009

Problem

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