To formulate the linear equation representing the situation described, we need to define the variables and relationships clearly.
Let:
- \( n \) be the number of people in attendance at a game.
- \( C \) be the total revenue earned from ticket sales.
Given:
- The ticket price is $15.
- The gym can seat a maximum of 1,500 people.
The revenue \( C \) generated from selling \( n \) tickets (where each ticket costs $15) can be expressed as:
\[ C = 15n \]
This equation represents the total revenue as a function of the number of attendees \( n \). Since the maximum capacity is 1,500 people, \( n \) can take any value from 0 to 1,500.
Thus, the complete linear equation for the total revenue based on the number of attendees is:
\[ C = 15n \quad \text{(where } 0 \leq n \leq 1500\text{)} \]