Difference between revisions of "1985 AJHSME Problem 23"

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== Problem ==
 
== Problem ==
King Middle School has <math>1200</math> students.  Each pupil takes <math>5</math> classes a day.  Each teacher teaches <math>4</math> classes.  Each class has <math>30</math> students and <math>1</math> teacher.  How many teachers are there at King Middle School?   
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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</math> students and <math>1</math> teacher.  How many teachers are there at King Middle School?   
  
 
<math>\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 45 \qquad \text{(E)}\ 50</math>
 
<math>\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 45 \qquad \text{(E)}\ 50</math>

Latest revision as of 02:11, 15 January 2025

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.