In 2020 , there were 12,900 students at college A, with a projected enrollment increase of 500 students per year. In the same year, there were 24,150 students at college B, with a projected enrollment decline of 750 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?
In the year the enrollment at both colleges will be the same.
The total enrollment at each college will be students.

If enrollment at A in 2020 is 12,900, increasing at 500 per year, and enrollment at B is 24,150, decreasing at 750 per year, you want to know the year the enrollments are the same, and what that enrollment is.

Setup

We can write equations for the enrollment as a function of year for each college:

A = 12900 +500(x -2020)
B = 24150 -750(x -2020)

where x is the year, and A, B are the enrollments.

Solution

We have A = B when ...

A = B

12900 +500(x -2020) = 24150 -750(x -2020)

1250(x -2020) = 11250 . . . . . . . . add 750(x -2020) -12900

x -2020 = 9 . . . . . . . . . . . . . . . divide by 1250

x = 2029

A = 12900 +500(9) = 17400

In the year 2029, enrollment at both colleges will be 17,400 students.