Modeling Ticket Sales with Linear Equations

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Questions and Answers

At the Orpheum Auditorium, main floor seats cost $14 and balcony seats cost $10. What does y represent in the equation $14x + 10y = 8600$, given a total revenue of $8600?

  • The total number of seats in the auditorium.
  • The number of balcony seats sold. (correct)
  • The number of main floor seats sold.
  • The profit made from selling all the seats.

An opera house sells main floor tickets for $14 and balcony tickets for $10. If the goal is to collect exactly $8600 in revenue, what equation correctly represents the relationship between x, the number of main floor tickets sold, and y, the number of balcony tickets sold?

  • $10x + 14y = 8600$
  • $24(x + y) = 8600$
  • $x + y = 8600$
  • $14x + 10y = 8600$ (correct)

An auditorium charges $14 for main floor seats and $10 for balcony seats. If they need to collect $8600 to cover expenses, which variable assignment correctly sets up the equation $14x + 10y = 8600$?

  • `x` = number of main floor seats, `y` = number of balcony seats (correct)
  • `x` = price of main floor seats, `y` = price of balcony seats
  • `x` = total revenue, `y` = total expenses
  • `x` = number of balcony seats, `y` = number of main floor seats

The Orpheum Auditorium sells tickets for an opera. Main floor seats are $14 and balcony seats are $10. The auditorium wants to determine how many of each type of seat they need to sell to reach $8600 in revenue. Which inequality could be used if the auditorium wants to exceed their revenue goal?

<p>$14x + 10y &gt; 8600$ (A)</p> Signup and view all the answers

An opera house needs to make $8600 from ticket sales to cover costs. Main floor seats sell for $14 and balcony seats sell for $10. If they sell 300 main floor seats, what is the minimum number of balcony seats they must sell to cover costs?

<p>440 (A)</p> Signup and view all the answers

At a recent opera performance, all 600 balcony seats were sold for $10 each. Main floor seats were $14 each. Using the equation $14x + 10y = 8600$, how many main floor seats (x) need to be sold to reach the $8600 revenue target?

<p>Approximately 186 seats (D)</p> Signup and view all the answers

An auditorium sells two types of tickets: main floor and balcony. Main floor tickets are priced at $14 and balcony tickets at $10. On a particular night, the auditorium sold 'x' main floor tickets and 'y' balcony tickets, reaching a total revenue of $8600. If the number of main floor tickets sold was doubled and the number of balcony tickets remained the same, which expression represents their new total revenue?

<p>$28x + 10y$ (D)</p> Signup and view all the answers

An opera house aims to collect $8600 from ticket sales. Main floor tickets cost $14, and balcony tickets cost $10. If the number of main floor tickets sold is 100 fewer than the number of balcony tickets sold, which system of equations could be used to determine the number of each type of ticket sold?

<p>$14x + 10y = 8600$ and $y = x + 100$ (C)</p> Signup and view all the answers

The Orpheum Auditorium needs to bring in $8600 from ticket sales. Main floor tickets are sold at $14 each, and balcony tickets are sold for $10 each. Which of the following represents the domain for 'x' (the number of main floor tickets sold) if the auditorium only sells whole tickets?

<p>All non-negative integers less than or equal to 614 (B)</p> Signup and view all the answers

An opera is being held at the Orpheum Auditorium. Main floor tickets are sold at $14 each, and balcony tickets are sold at $10 each. The equation representing ticket sales is $14x + 10y = 8600$. If it is known that at least 200 balcony tickets need to b sold, which of the following inequalities represents the possible number of main floor tickets?

<p>$x \le 471$ (C)</p> Signup and view all the answers

Flashcards

Ticket Sales Equation

x = # of main floor seats, y = # of balcony seats. Equation: 14x + 10y = 8600.

What does $8600 represent?

Represents the total amount of money needed from ticket sales to cover the opera's expenses.

Cost of main floor seats

Each main floor seat costs $14.

Cost of Balcony Seats

Each balcony seat costs $10.

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Study Notes

  • Tickets to an opera at the Orpheum Auditorium cost $14 for main floor seats and $10 for balcony seats.

  • $8600 must be collected to meet expenses.

  • If x = number of main floor seats, and y = number of balcony seats, then: 14x + 10y = 8600

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