word problem

Question

Consider the following enrollment data for Red Rock Community College.

3321 Evening Male students enrolled in 2005 and 3097 Evening Male students enrolled in 2003.

4003 Evening Female students enrolled in 2005 and 3833 Evening Female students enrolled in 2003.

For each student population, find a linear model such that x

E represents the years after 2000 and

E represents the enrollment.

The linear model for Evening Male Enrollment:?

The linear model for Evening Female Enrollment:?

In what year will these enrollments be the same?

Answer 1

Ladies first.....

slope M = (4003 - 3833)/(2005 - 2003) = 170/2 = 85

85 students per year.

Since y = Mx + b ---> then b = y - M*x

Using ( 2003, 3833) with M=85, the intercept b is

b = 3833 - 85*2003 = -166422

so the linear model is E (x) = 85*x - 166422



Now for the guys:

(2003, 3097) and (2005, 3321)

The slope M = (3321 - 3097)/(2005 - 2003) = 224/2 = 112

B = y - m*x = 3097 - 112*2003 = -221239

The linear model is E(x) = 112X - 221239

You can check these line equations by plugging in 2005. It works!

Now , it's time to find when the lines will be equal.

112 X - 221239 = 85 X - 166422

112X - 221239 - 85X + 166422 = 0

27X - 54817 = 0

X = 54817/27 = 2030.259259259.... (Sometime in APril 2030)

At that time the population/enrollment will be 6150.