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.

## Answer This Question

## Related Questions

- Math - School A has 480 students and 16 classrooms. School b has 192 students ...
- Math - School A has 480 students and 16 classrooms, School B has 192 students ...
- After-school activities for high school students - I recently received a job to...
- statistics - A survey about the art program at a school found that 250 students ...
- Math - The table shows the number of classrooms needed for different numbers of ...
- Algebra - 69% of the students at a school are involved in after-school ...
- math - can you help ; i need to write and solve for each situation. check the ...
- math - If 70% of the students at a school sign up for exercise Day, a sporting ...
- Business math - The clarkdell school system has three schools. School #1 has 500...
- graphs and angles - a survey about students government program at a school found...

More Related Questions