To represent the budget constraints for the event at Stars and Strikes Bowling, we can express the costs in terms of the variables \(x\) (the number of people attending) and \(y\) (the number of hours spent).
The cost for entrance is \(15x\) (since it costs $15 per person), and the cost for bowling is \(20y\) (since it costs $20 per hour).
The total cost must be within the budget of $200, which gives us the following inequality:
\[ 15x + 20y \leq 200 \]
This inequality represents the total cost of the event in terms of the number of attendees and the hours spent bowling, ensuring that it does not exceed the budget.