Please help with this question

Question

In​ 2020, there were 15,800 students at college​ A, with a projected enrollment increase of 500 students per year. In the same​ year, there were 33,800 students at college​ B, with a projected enrollment decline of 1000 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 = number of years from 2020 that it takes for the colleges to have the same enrollment

15800 + 500x = 33800 - 1000x

1500x = 18000

x = 180/15 = 12 years

The colleges will have the same enrollment in the year 2032.

Answer 2

I agree with Mark M’s solution. The colleges will have the same enrollment in the year 2032. The question also asks what the enrollment in each college will be at that time.

To find that answer, plug 12 (years) into the original equation.

15,800 + 500x = 33,800 - 1,000x

15,800 + 500*12 = 33,800 - 1,000*12

15,800 + 6,000 = 33,800 -12,000

21,800 = 21,800

So we can see that each college will have an enrollment of 21,800 students in the year 2032.