In 2000, there were 12900 students at college A, with a projected enrollment increase of 900 students per year. In the same year, there were 25,000 students at college B, with a projected enrollment decline of 700 students per year. In what year will the two colleges have the same enrollment?

Question

Mathematics

Enrique Rocha

21 March, 08:10

In 2000, there were 12900 students at college A, with a projected enrollment increase of 900 students per year. In the same year, there were 25,000 students at college B, with a projected enrollment decline of 700 students per year. In what year will the two colleges have the same enrollment?

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Answers (1)

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Vaughn Faulkner · Answer 1

Step-by-step explanation:

Let x represent the number of years it will take the two colleges to have the same enrollment.

In 2000, there were 12900 students at college A, with a projected enrollment increase of 900 students per year. This means that the expected number of students at college A in x years time is

12900 + 900x

In the same year, there were 25,000 students at college B, with a projected enrollment decline of 700 students per year. This means that the expected number of students at college B in x years time is

25000 - 700x

For both colleges to have the same enrollment,

12900 + 900x = 25000 - 700x

900x + 700x = 25000 - 12900

1600x = 12100

x = 12100/1600

x = 7.56

Approximately 8 years

The year would be 2000 + 8 = 2008