Question

In​ 2020, there were 18,500 students at college​ A, with a projected enrollment increase of 1250 students per year. In the same​ year, there were 37,750 students at college​ B, with a projected enrollment decline of 500 students per year. According to these​ projections, when will the colleges have the same​ enrollment? What will be the enrollment in each college at that​ time?

Answer 1

Let x be the number of years from 2020.

For college A: Number of students = 18,500 + 1,250x
For college B: Number of students = 37,750 - 500x

Setting them equal to each other:

18,500 + 1,250x = 37,750 - 500x

1,750x = 19,250

x = 11

Therefore, in 11 years from 2020, the colleges will have the same enrollment.

Substitute x = 11 into the equations:

For college A: 18,500 + 1,250(11) = 32,000 students
For college B: 37,750 - 500(11) = 32,250 students

So, in 11 years from 2020, both colleges will have an enrollment of 32,000 students.