SOLUTION: There are 100 people in a room, including only teachers and students. They are trying to share 100 bags of sweets. As a result, each teacher has 3 bags of sweets where every 3 stud

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Question 681902: There are 100 people in a room, including only teachers and students. They are trying to share 100 bags of sweets. As a result, each teacher has 3 bags of sweets where every 3 students share one bag of sweets. How many teachers and students are there?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
There are 100 people in a room, including only teachers and students. They are trying to share 100 bags of sweets. As a result, each teacher has 3 bags of sweets where every 3 students share one bag of sweets. How many teachers and students are there?

 Let t = the number of teachers
 Let s = the number of students

There are 100 people in the room, so one equation is 

 t + s = 100

each teacher gets a whopping 3 bags and each student gets only 1%2F3rd of a bag.

So the number of bags given to teachers is 3 times the number of teachers,
or 3t bags

and

the number of bags given to students is 1%2F3 times the number of
students, or 1%2F3s.

There are 100 bags, so the other equation is

3t + 1%2F3s = 100

So the system of equations is:

system%28t%2Bs=100%2C3t%2Bexpr%281%2F3%29s=100%29

Can you solve that for t and s? If not post again
asking how to do it.

Solution: 25 teachers hogging 75 bags and 75 poor students 
having to share the remaining 25 bags. 'Taint fair!

[Maybe the students are obese and the teachers are thin! lol]

Edwin