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.
Answer This Question
Related Questions
 English Expression  Welcome to Namsan Middle School in Seoul. There are 500 ...
 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 ...
 English  1. Our school has a great audiovisual room. If Mohamed visits our ...
 Afterschool 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 afterschool ...
 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 ...
More Related Questions