Question

In 2004, there were 14,100 students at college A, with a projected enrollment increase of 1200 students per year. In the same year, there were 37,500 students at college B, with a projected

enrollment decline of 600 students per year.
According to these projections, when will the colleges have the same enrollment? What will be the enrollment at that time?
Saw

Answer 1

Both colleges will have the same enrollment after 13 years ie in the year 2017

At this point in time total enrollment in either college will be 29,700

Explanation:

Let X represent the number of years after 2004 when both enrollments are the same

For college A

Increase in enrollment = 1200X

Total enrollment after X years = 14100 + 1200X (1)

For college B

Decline in enrollment after X years = 600X

Total enrollment after X years = 37500 - 600X (2)

Setting (1) = (2) we can solve for X

14100 + 1200X = 37500-600X

Adding 600X on both sides,

14100+1200X + 600X = 37,500 -600X + 600X

14100 + 1800X = 37500

Subtracting 14100 on both sides

1800X = 37500-14100

1800X = 23400

X = 23400/1800 = 13

So both enrollments will be the same after 13 years ie in the year 2004 + 13 = 2017

We can find out the total enrollment at either college by plugging in this value of X =13 in either Equations (1) or (2)

For college A, this would be 14100 + 1200(13) = 14100 + 15600 = 29,700

We know this should also be the enrollment at college B, but just to make sure our calculations are OK, let's plug in X=13 into equation 2

Total enrollment at college B = 37500-600(13) = 37500-7800 = 29,700

So our computations are correct