Posted by Lana on Tuesday, December 13, 2011 at 1:19am.
I need help with a Matrix Algebra problem
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, onefifth of the students in room B move to room C, and onethird 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?
Thanks

PreCalculus  Steve, Tuesday, December 13, 2011 at 12:07pm
to start,
a+b+c = 100
After the room changes, we have
a/2 + c/3 = a
4b/5 + a/2 = b
2c/3 + b/5 = c
or,
a/2 = c/3
a/2 = b/5
b/5 = c/3 = a/2
so, substituting in,
a + 5a/2 + 3a/2 = 100
2a + 5a + 3a = 200
a = 20
b = 50
c = 30
during the move, 10 students move to each room.