   Chapter 11.1, Problem 72E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# APPLICATIONSClassroom Use 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?

To determine

To find:

The number of students occupying room A, B, and C.

Explanation

Given:

The total number of students in classrooms A, B, and C is 100. 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. The total number of students in each room is the same for both periods.

Calculation:

Let x, y, and z represents the number of students in class A, B, and C.

The system of equations is given by,

x+y+z=100x2+z3=0x2y5=0y5z3=0

Consider the system of equations,

{x+y+z=100x2+z3=0x2y5=0y5z3=0

The augmented matrix obtained is,



Transform the augmented matrix into row echelon form.

Perform the transformation R4R2+R4 and R4R3+R4.



Remove the last row as all the elements are zero.

Perform the transformation R2R3+R2 and R3R3R2.



Perform the transformation R1R1+5R2

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