In 2020, there were 16,800 students at college A, with a projected enrollment increase of 1250 students per year. In the same year, there were 28,800 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?
To find when the colleges will have the same enrollment, we can set up a system of equations.
Let x be the number of years from 2020.
College A enrollment: 16,800 + 1,250x
College B enrollment: 28,800 - 750x
Setting them equal to each other:
16,800 + 1,250x = 28,800 - 750x
Adding 750x to both sides:
16,800 + 2,000x = 28,800
Subtracting 16,800 from both sides:
2,000x = 12,000
Dividing by 2,000:
x = 6
In 6 years, or by the year 2026, the colleges will have the same enrollment.
To find the enrollment in each college at that time:
College A enrollment in 2026: 16,800 + 1,250(6) = 16,800 + 7,500 = 24,300 students
College B enrollment in 2026: 28,800 - 750(6) = 28,800 - 4,500 = 24,300 students
Therefore, in 2026, both colleges will have 24,300 students.