SOLUTION: In a class that has 375 students, the average on an exam was exactly 55.15. If all students earned integer scores from 0 to 100, what is the minimum number of students that could h

Algebra ->  Average -> SOLUTION: In a class that has 375 students, the average on an exam was exactly 55.15. If all students earned integer scores from 0 to 100, what is the minimum number of students that could h      Log On


   

Question 601665: In a class that has 375 students, the average on an exam was exactly 55.15. If all students earned integer scores from 0 to 100, what is the minimum number of students that could have taken the exam, and what is the maximum number of students that could have taken the exam?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the students scores (sum) is an integer that divided buy the number (n) of students taking the exam is 55.15
sum%2Fn=55.15 --> sum=55.15n=%285515%2F100%29%2An
We can transform that fraction into one in lowest terms
5515%2F100=1103%2F20 and write
sum=%281103%2F20%29%2An
Any n that is not a multiple of 20 would divide by 20 giving a quotient q and a remainder r<20, with
n=20q%2Br and sum=%281103%2F20%29%2A%2820q%2Br%29=1103q%2B1103%2Ar%2F20 would not be an integer.
If, and only if, n is a multiple of 20, will sum=%281103%2F20%29%2An be an integer.
The number of students taking the exam could have been 20, 40, 60, ..., 340, or 360.
The minimum number of students that could have taken the exam is highlight+%2820%29, and the maximum number of students that could have taken the exam is highlight%28360%29 .