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# AMC 8 1985 Problem 23

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https://artofproblemsolving.com/wiki/index.php/1985_AJHSME_Problems/Problem_23

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?

I don't understand the solution- Could somebody help????

Like just explain a hint please!

SOLUTION (BY AOPS)

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

Each class has 30 students, so there must be 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

t=50

This is answer choice E (50)

EDIT:

I don't get the 6000/30- that's it!

Nov 13, 2019
edited by tommarvoloriddle  Nov 13, 2019
edited by tommarvoloriddle  Nov 13, 2019

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like they established already that 6000 comes from the 1200 students with the total of 5 classes among them....

soo,,,,,, and we originally know that in EACH class there is a total of 30 students so...... in order to find the ACTUAL number of classes

you had to take that 6000 and divide it by 30 bc you know that you have 6000 students and you also know that each class has thirty so...

30x = 6,000

think of it like that :D

Nov 13, 2019
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excuse my trash grammar btw im really braindead and tired :')

Nirvana  Nov 13, 2019
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Hi Tom...riddle

Thanks Nirvana

I am going to say the same thing as Nirvana but  use slightly  different words.

(not better words, just different words)

There are 1200 students but you can think of this as 1200*5 faces in front of teachers.

So we have 6000 enthusiastic faces holding on to every word the teachers' say (in my dreams)

There are 30 faces in each class so there must be 6000 divided by 30 = 200classes

Each teacher teaches 4 of these so there are  200 divided by 4 = 50 teachers.

Nov 13, 2019
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:O

OH, Thank you!

tommarvoloriddle  Nov 13, 2019