WORd problems

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:

 

E=

The linear model for Part-Time Female Enrollment:

 

E=

In what year will these enrollments be the same?

 

 

Answer 1

To find the model for part time male enrollment, we can use the data points (2, 3774) and (10, 4430) to find the equation of a line.  To find the slope:

m = (4430 - 3374)/(10-2) = 132

To find the equation of the line, y = mx + b, we plug in a data point:

3774 = 132(2) + b

b = 3510

Therefore, the linear model for male part time enrollment is:

y = 132x + 3510

 

Do the same for the female enrollment using the data point (2, 4516) and (10, 5028).  

m = (5028-4516)/(10-2) = 64

 

y = 64x + b

4516 = 64*2 + b

b = 4388

 

The model for female part time enrollment is y = 64x + 4388

 

To find the year that enrollment will be the same, set these two equations equal to each other and solve for x.

 

64x + 4388 = 132x + 3510

 

Subtracting 3510 from both sides:

 

64x + 878 = 132x

 

Subtracting 64x from both sides:

 

68x = 878

 

Divide both sides by 68x:

 

x = 12.9 years --> round up to 13 years.

 

Enrollment will be the same in 2013.

 

Hope this helps!