To represent the situation with an inequality, we can use the following equation based on the total cost of renting the hall:
Cost = Flat fee + (Hourly rate × Number of hours)
In this case, the cost to rent the hall is given by:
\[ \text{Cost} = 200 + 25h \]
where \( h \) is the number of hours Mary rents the hall. Since Mary has a budget of $500, we can set up the inequality:
\[ 200 + 25h \leq 500 \]
Now, we will solve this inequality for \( h \):
- Subtract 200 from both sides:
\[ 25h \leq 500 - 200 \]
\[ 25h \leq 300 \]
- Now, divide both sides by 25:
\[ h \leq \frac{300}{25} \]
\[ h \leq 12 \]
Thus, the maximum number of hours Mary can rent the hall without exceeding her budget is 12 hours.