A company that teaches self-improvement seminars is holding one of its seminars in Oakland. The company pays a flat fee of $300 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $20 to purchase books and supplies. Each attendee will pay $80 for the seminar. Once a certain number of attendee register, the company will be breaking even. How many attendees will that take?
Write a system of equations, graph them, and type the solution.
Let's assume that the number of attendees needed for the company to break even is represented by x.
Equation 1: Total cost = Total revenue
The total cost for the company includes the facility rental fee and the cost of books and supplies, which is given by:
300 + 20x
The total revenue for the company is obtained by multiplying the number of attendees by the amount paid by each attendee:
80x
Given that the total cost and total revenue are equal, we can write the equation as:
300 + 20x = 80x
Simplifying this equation, we have:
300 = 60x
Dividing both sides by 60, we get:
x = 5
Therefore, the company will need 5 attendees to break even.
Graphically, the system of equations can be represented by two lines:
y1 = 300 + 20x
y2 = 80x
To find the point of intersection, we can graph the two equations and find the x-coordinate where they meet. Upon graphing, we find that the lines intersect at x = 5.
Hence, the solution is x = 5.