A local theater is planning to host a play. The theater has 300 seats available, and it sells two types of tickets standard tickets (s) and premium tickets (p) the theater wants to find a combination of ticket sales that exactly fills the theater each standard ticket sold allows for 1 attendee while each premium ticket sold allows for 2 attendees. Part 1 create a two variable linear equation that represents the total number of attendees when all the seats are filled clearly define your variables

Question

Part 2 the theater sells 100 standard tickets and 100 premium tickets determine of this ticket sales decision exactly fills the theater show your work and state whether the theater is filled with this given scenario

Answer 1

Part 1: Creating the Linear Equation

Define the Variables:

• Let \( s \) = the number of standard tickets sold.
• Let \( p \) = the number of premium tickets sold.

Linear Equation:

• Each standard ticket allows for 1 attendee, and each premium ticket allows for 2 attendees. Since the theater has a total of 300 seats, the equation representing the total number of attendees is:

\[ s + 2p = 300 \]

Part 2: Determine if the Ticket Sales Decision Fills the Theater

Given Ticket Sales:

• Number of standard tickets sold, \( s = 100 \)
• Number of premium tickets sold, \( p = 100 \)

Calculate the Total Number of Attendees: Substituting the values into the equation:

\[ s + 2p = 100 + 2(100) = 100 + 200 = 300 \]

Conclusion: Since the total calculated number of attendees is exactly 300, the theater is indeed filled with this given ticket sales decision.