a company that teaches self - improvement seminars is holding one of its seminars in princeton. the company…

a company that teaches self - improvement seminars is holding one of its seminars in princeton. the company pays a flat fee of $600 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 $50 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.

a company that teaches self - improvement seminars is holding one of its seminars in princeton. the company pays a flat fee of $600 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 $50 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.

Answer

Explanation:

Step1: Define the cost and revenue functions

Let (x) be the number of attendees. The cost function (C(x)) is the sum of the fixed cost and the variable cost. The fixed cost is (600) (for renting the facility), and the variable cost is (20x) (for books and supplies per attendee). So, (C(x)=600 + 20x). The revenue function (R(x)) is based on the price per attendee. Each attendee pays (50), so (R(x)=50x).

Step2: Set up the break - even equation

At the break - even point, cost equals revenue, i.e., (C(x)=R(x)). Substitute the functions: (600+20x = 50x).

Step3: Solve the equation for (x)

Subtract (20x) from both sides: (600+20x-20x=50x - 20x) (600 = 30x). Divide both sides by (30): (x=\frac{600}{30}).

Answer:

(20)