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.

Answer 1

Let's define the variables as follows:

• Let \( S \) represent the number of standard tickets sold.
• Let \( P \) represent the number of premium tickets sold.

Each standard ticket allows for 1 attendee, and each premium ticket allows for 2 attendees. Therefore, the total number of attendees can be represented by the equation:

\[ S + 2P = 300 \]

This equation states that the total number of attendees (the number of standard ticket holders plus twice the number of premium ticket holders) must equal the total number of seats available, which is 300.