Question

In​ 2005, there were 14,100 students at college​ A, with a projected enrollment increase of 750 students per year. In the same​ year, there were 42,100 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?

Answer 1

(a)2019 (14 years after)

(b)24,600

Explanation:

Let the number of years =n

College A

Initial Population in 2005 = 14,100

Increase per year = 750

Therefore, the population after n years = 14,100+750n

College B

Initial Population in 2005 = 42,100

Decline per year = 1250

Therefore, the population after n years = 42,100-1250n

When the enrollments are the same

14,100+750n=42,100-1250n

1250n+750n=42100-14100

2000n=28000

n=14

Therefore, in 2019 (14 years after), the colleges will have the same​ enrollment.

Enrollment in 2019 =42,100-1250(14)

=24,600

Answer 2

Set up two equations and set equal to each other. Let number of years = x:

College A = 14100+750x

College B = 42100-1250x

Set equal:

14100 + 750x = 42100 - 1250x

Subtract 750x from both sides:

14100 = 42100 - 2000x

Subtract 42100 from both sides:

-28000 = -2000x

Divide both sides by -2000:

x = -28000 / -2000

x = 14

It will take 14 years for the schools to have the same enrollment.

Enrollment will be:

14100 + 750(14) = 14100 + 10500 = 24,600