Question

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. (5 Points)



Part 2: The theater sells 100 standard tickets and 100 premium tickets. Determine if 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
Let S = number of standard tickets sold (1 attendee each).
Let P = number of premium tickets sold (2 attendees each).
Equation: S + 2P = 300.

Part 2
Given S = 100 and P = 100, substitute into the equation:
100 + 2(100) = 100 + 200 = 300.
Since this equals 300 seats, the theater is exactly filled.