Question

A. Edmonds Community College is opening a five credit hour section of Business Pre-Calculus for thewinter quarter. An instructor and room for the quarter cost $12,700. Additionally, it costs $31.00 perstudent per quarter after the matching money from the state is considered. The college charges $83 per credit hour. Being a non-profit, they just need to break even in each class. What is the minimum numberof students they need to let the section run?Minimum Number of Students_____Round your answer UP to the nearest wholenumber.

Answer 1

Let's list down the given information in the question.

Instructor and a room = $12, 700

Cost per student = $31.00

Cost per credit hour = $83

If the charge per credit hour is $83 and the section to be run is for 5 credit hours then, total charge is $83 x 5 = $415. This means every student will have to pay $415 for the subject Business Precal.

On the other hand, the college spent $12700 for the instructor and the room as well as $31 per student.

Assuming that x = the number of students, then we can have the equation below:

`12,700+31x\leq415x`

where 31x is the cost per student per quarter and 415x is the charge per student for the subject Business Precal. The cost of the school must be less than or equal to its total charges to the school.

From that inequality, let's solve for x.

`\begin{gathered} 12,700+31x\leq415x \\ \text{Subtract 31x on both sides.} \\ 12,700\leq384x \\ \text{Divide both sides by 384.} \\ 33.07\leq x \\ 34\leq x \end{gathered}`

Hence, the minimum number of students they need to let the section is 34.

At 34 students, the school will be able to spend $13, 754 and its total charges to the student is $14, 110.

Whereas, at 33 students, the school will be able to spend $13, 723 but their total charges to the student is only $13, 695.

Hence, they need at least 34 students in order to run the section Business PreCal.