SOLUTION: A small school has 100 students who occupy three classrooms: A, B, and C. After the first period of the school day, half the students in room A move to room B, one-fifth of the stu

Algebra ->  Equations -> SOLUTION: A small school has 100 students who occupy three classrooms: A, B, and C. After the first period of the school day, half the students in room A move to room B, one-fifth of the stu      Log On


   

Question 1198569: A small school has 100 students who occupy three classrooms: A, B, and C. After the first period of the school day, half the students in room A move to room B, one-fifth of the students in room B move to room C, and one-third of the students in room C move to room A.
Nevertheless, the total number of students in each room is the same for both periods. How many students occupy each room?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a%2Bb%2Bc+=+100
After the room changes, we have
a%2F2+%2B+c%2F3+=+a
4b%2F5+%2B+a%2F2+=+b
2c%2F3+%2B+b%2F5+=+c
or,
a%2F2+=+c%2F3
a%2F2+=+b%2F5
b%2F5+=+c%2F3+=+a%2F2
so, substituting in a%2Bb%2Bc+=+100
a+%2B+5a%2F2+%2B+3a%2F2+=+100
2a+%2B+5a+%2B+3a+=+200
10a+=+200
a+=+20
since
a%2F2+=+b%2F5
20%2F2+=+b%2F5
100%2F2+=+b
b+=+50
and
c+=+100-%2820%2B50%29
c+=+100-70
c+=+30

20 students occupy room a
50 students occupy room b
30 students occupy room c

during the move, 10 students move to each room