I need help with a matrix algebra problem A small school has 100 students occupying three classrooms A, B, and C. After the first period of the school day, half of the students in room A move out in Hall B, one-fifth of the students in Hall B move to Hall C, and one-third of the students in Hall C move to Hall A. Nevertheless, the total number of students in each hall is the same for both periods. How many students occupy each room?
Please start,
a+b+c = 100
After the room change, we have
a/2 + c/3 = a
4b/5 + a/2 = b
2c/3 + b/5 = c
Where,
a/2 = c/3
a/2 = b/5
b/5 = c/3 = a/2
so, replacing in,
one + 5a/2 + 3a/2 = 100
2a + 5a + 3a = 200
one = 20
b=50
c = 30
during the move, 10 students move into each room.