Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.A company that teaches self-improvement seminars is holding one of its seminars in Oxford. The company pays a flat fee of $104 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $18 to purchase books and supplies. Each attendee will pay $26 for the seminar. Once a certain number of attendee register, the company will be breaking even. How many attendees will that take? What will be the company's total expenses and revenues?

Answer 1

Let:

y = Total cost

x = Number of attendees

b = Flat fee = 104

a = Cost of books = $18

c = Payment of each attendee = $26

The cost function will be given by:

`\begin{gathered} y=b+ax \\ y=104+18x \end{gathered}`

The revenue function will be:

`\begin{gathered} r=cx \\ r=26x \end{gathered}`

In order to the company will be breaking even:

`\begin{gathered} y=r \\ so\colon \\ 104+18x=26x \end{gathered}`

Solve for x:

`\begin{gathered} 26x-18x=104 \\ 8x=104 \\ x=(104)/(8) \\ x=13 \end{gathered}`

It will take 13 attendees and the company's total expenses and revenues at that point is:

`13\cdot26=338`

$338

Answer:

13 attendees and $338