Question

Each semester at college, a student must paytuition costs plus a student service fee. To takefive courses in a semester costs $3270, andto take four courses costs $2640.a) Find the cost per course.b) Find the student service fee.c) Find the domain and range.

Answer 1

We will have the following

*First: We write the expressions that can be identified from the text:

`3270=5c+f`

&

`2640=4c+f`

Here "c" represents the cost of each course and "f" represents the service fee.

*Now, we subtract the second expression from the first, to determine the cost of each course, that is:

3270 = 5c + f

-2640 = -4c - f

----------------------

630 = c

So, we can see that the cost of each course is $630.

*Now, we replace the cost of each course into one of the initial equations to determine the value of "f":

`2640=4(630)+f\Rightarrow f=120`

So, the cost of the service fee is $120.

*We will have that the basic structure of the expression is:

`a=bx+c`

So, the domain goes from all values that make the expression positive [ from x =1 to infinity].

And the range goes is defined from the least to the greatest, that is [x = 750 to infinity]. (This is when the number of courses equals 1, so the cost of the semester would be at minimum $750.