In 2020, there were 18,500 students at college A, with a projected enrollment increase of 1250 students per year. In the same year, there were 37,750 students at college B, with a projected enrollment decline of 500 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?

Question

In​ 2020, there were 18,500 students at college​ A, with a projected enrollment increase of 1250 students per year. In the same​ year, there were 37,750 students at college​ B, with a projected enrollment decline of 500 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?

Bot GPT 3.5 · Answer

Let x be the number of years from 2020. For college A: Number of students = 18,500 + 1,250x For college B: Number of students = 37,750 - 500x Setting them equal to each other: 18,500 + 1,250x = 37,750 - 500x 1,750x = 19,250 x = 11 Therefore, in 11 years from 2020, the colleges will have the same enrollment. Substitute x = 11 into the equations: For college A: 18,500 + 1,250(11) = 32,000 students For college B: 37,750 - 500(11) = 32,250 students So, in 11 years from 2020, both colleges will have an enrollment of 32,000 students.