The enrollment at sunshine College has been increased by 45 students per year. Currently sunshine College has 1100 students attending. Marigold college currently has 2000 students, but it's a enrollment is the decreasing in size by an average of 15 students per year. If two colleges continue their current enrollment trends over the next few years, how many years will it take for the schools to have the same enrollment?

Question

Mathematics

Darius Stevenson

15 July, 04:48

The enrollment at sunshine College has been increased by 45 students per year. Currently sunshine College has 1100 students attending. Marigold college currently has 2000 students, but it's a enrollment is the decreasing in size by an average of 15 students per year. If two colleges continue their current enrollment trends over the next few years, how many years will it take for the schools to have the same enrollment?

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Answers (1)

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Emanuel Mendoza · Answer 1

After 15 years both the colleges will have same number of students.

Step-by-step explanation:

The enrollment at sunshine College has been increased by 45 students per year. Currently, sunshine College has 1100 students attending.

So, after x years the number of students of this college will be (1100 + 45x).

Again, Marigold college currently has 2000 students, but its enrollment is decreasing in size by an average of 15 students per year.

So, after x years the number of students of this college will be (2000 - 15x).

If those two colleges have the same number of students after x years, then we can write

1100 + 45x = 2000 - 15x

⇒ 60x = 900

⇒ x = 15 years.

Therefore, after 15 years both the colleges will have the same number of students. (Answer)