Word problem

Question

Consider the following enrollment data for Juniper Community College.

3774 Part-Time Male students enrolled in 2002 and 4430 Part-Time Male students enrolled in 2010.

4516 Part-Time Female students enrolled in 2002 and 5028 Part-Time Female students enrolled in 2010.

For each student population, find a linear model such that x
represents the years after 2000 and E
represents the enrollment.

The linear model for Part-Time Male Enrollment:


The linear model for Part-Time Female Enrollment:


In what year will these enrollments be the same?

Answer 1

For the male enrollment:

(2,3774)
(10,4430)

The slope is (4430 - 3774) / (10-2) = 656/8 = 82

So 82 new students every year.

THe intercept must be 3774 - 2 * 82 = 3610

E = 82X + 3610

For the female enrollment:

(2,4516) and (10,5028)

The slope is (5028 - 4516) / (10 -2) = 512/8 = 64

So 64 new students per year.

The intercept must be 4516 - 64 x 2 = 4388

E= 64X + 4388



Based on the models, the enrollment will be equal at:

82X + 3610 = 64X + 4388

Moving everything to left side, changing the signs:

82X + 3610 - 64X - 4388 = 0

18X - 778 = 0

18X = 778

X = 778/18 = 389/9 = 43 and 2/9 = 43.222222

7154 and 2/9 shall be the enrollment