In 2020, there were 18,500 students at college A, with a projected enrollment increase of 1000 students per year. In the same year, there were 36,500 students at college B, with a projected enrollment decline of 1250 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 the following equation:
18,500 + 1000x = 36,500 - 1250x
Where x represents the number of years from 2020.
Now, let's solve for x:
18,500 + 1000x = 36,500 - 1250x
18,500 + 1250x = 36,500
1250x = 18,000
x = 18,000 / 1250
x = 14.4
This means that in 14.4 years, the colleges will have the same enrollment. Since we can't have a fraction of a year, we will round up to the nearest whole number, which means it will take 15 years.
Now, let's find the enrollments in each college at that time:
For College A:
18,500 + 1000(15) = 33,500 students
For College B:
36,500 - 1250(15) = 18,250 students
Therefore, in 15 years, both colleges will have an enrollment of 33,500 students.