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.

Question

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. (2 points)

make it short and use simple terms

GPT-4o mini · Answer

### Part 1: Linear Equation **Variables:** - Let $ S $ = number of standard tickets sold - Let $ P $ = number of premium tickets sold **Equation:** Since each standard ticket allows 1 attendee and each premium ticket allows 2 attendees, the total number of attendees can be represented by the equation: $$ S + 2P = 300 $$ This equation means that the total number of attendees from standard and premium tickets combined must equal the 300 seats in the theater. --- ### Part 2: Ticket Sales Scenario **Given:** - Standard tickets sold $ S = 100 $ - Premium tickets sold $ P = 100 $ **Calculate total attendees:** Using the equation from Part 1: $$ 100 + 2(100) = 100 + 200 = 300 $$ **Conclusion:** The total number of attendees is 300, which exactly fills the theater. Therefore, the theater is filled with this ticket sales decision.