Write a system of equations

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

A company that teaches self-improvement seminars is holding one of its seminars in Sparrowtown. The company pays a flat fee of $120 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $3 to purchase books and supplies. Each attendee will pay $15 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?

Once___  attendees have registered, the company's expenses and receipts will both total $___.

Answer 1

So we have two equations here, one being the cost, and one being the profit. Both are functions of x attendees.

The cost is 120$ + 3$ per attendee, or:

C(x) = 3x + 120

The profit is 15$ per attendee, or:

P(x) = 15x

Now, to find where these two functions are equal, you must set them equal to each other.

3x + 120 = 15x

Now solve:

3x - 15x = -120 -----Move 15x to the left, 120 to the right side

-12x = -120 ----subtract 15x from 3x

x = 10 ------divide both sides by -12

x=10

The number of attendees needed is 10 to break even. To find what the total is, plug 10 into either equation.

3(10) + 120 = 150

15(10) = 150 ----Showing that both equal 150

The expenses and receipts total will be $150.

Hope this helps!