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, 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?

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.

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