In 2005, there were 12,300 students at college A, with a projected enrollment increase of 500 students per year. In the same year there were 18,550 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 the enrollment in each college at that time?

Answer: 5 years

14,800 students enrolled

Step-by-step explanation:

Let x represent the number of years and

Let y represent the number of students enrolled

College A: y = 12,300 + 500x

College B: y = 18,550 - 750x

Use substitution Method to solve:

12,300 + 500x = 18,550 - 750x

+750x + 750x

12,300 + 1250x = 18,550

-12,300 - 12,300

1250x = 6250

x = 5

Input x = 5 into one of the equations to solve for y.

y = 12,300 + 500x

= 12,300 + 500 (5)

= 12,300 + 2500

= 14,800