if the three schools have a total enrollment of 96,000 students, what is the enrollment at each school?

Question

The University of Texas at Austin has three times as many students enrolled as the University of Miami. The University of California, Berkley has 3,000 more than twice the number of students as the University of Miami.

Write the system of linear equations. 

Write the Augmented Matrix for the system of linear equations then solve using the Gauss-Jordan Elimination Method. Show all row operations and at least 5 of the resulting matrices. Use proper notation.

Please help solve this in Matrix form Thank you

Answer 1

A = 3M

B = 3000 + 2M

A+B + M = 96,000

3M + 3000+2 M + M = 96000

6M = 93,000

M = 15,500 at U of Miami

B = 34,000 at Berkeley

A = 46,500 at Austin

46.5+34 +15.5 = 96