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

Answer 1

Step-by-step explanation:

let the University of Miami enrolment be x

so the University of Texas at Austin has three times = 3x

The University of California, Berkley has 3,000 more than twice the number of students at the University of Miami.

this can be translated as = 3000+2x

in total, the enrolment is 96,000

therefore

x+3x+3000+2x=96000

we can now solve for x

6x=96000-3000

6x=93000

divide both sides by 6 we have

x=15500

1. The University of Miami enrolment is 15500 students

2. The University of Texas at Austin has three times = 3x

   =3*15500

   = 46500  students

3. The University of California, Berkley has

    = 3000+2x

    = 3000+2(15500)

    =3000+46500

    =49500 students