Question
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.
Write a system of equations, graph them, and type the solution.
Answers
GPT 3.5
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.
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.