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 Campbell. The company pays a flat fee of $208 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $2 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 $_____.

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 Campbell. The company pays a flat fee of $208 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $2 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 $_____.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables: Let x be the number of attendees. The company's total expenses (E) will be the sum of the flat fee and the cost of books and supplies per attendee. The company's total revenue (R) will be the amount each attendee pays times the number of attendees.Expenses Equation: Write the equation for the company's expenses: E = $208 (flat fee) + $2x (cost per attendee for books and supplies) So, the equation for expenses is: E = 2x + 208Revenue Equation: Write the equation for the company's revenue: R = $15x (revenue per attendee) So, the equation for revenue is: R = 15xSet Break-even Point: To find the break-even point, set the expenses equal to the revenue: 2x + 208 = 15xIsolate Variable: Solve for x by isolating the variable: Subtract 2x from both sides of the equation: 2x + 208 - 2x = 15x - 2x 208 = 13xSolve for x: Divide both sides by 13 to solve for x: 208 / 13 = 13x / 13 16 = xCalculate Total: Now that we have the number of attendees (x = 16), we can calculate the total expenses and revenues, which will be equal at the break-even point: E = R = 2(16) + 208 = 32 + 208 = $240Conclusion: Therefore, once 16 attendees have registered, the company's expenses and receipts will both total $240.

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