Question 1: Part 1: Write the two-step inequality that represents this situation.
Maria's total cost for renting the hall can be expressed as:
\[ \text{Total Cost} = \text{Base Fee} + (\text{Hourly Rate} \times \text{Number of Hours}) \]
Given her budget of $500, we can set up the inequality:
\[ 200 + 25h \leq 500 \]
Question 2: Part 2: Solve the inequality you wrote in part 1. Show/explain all steps including your inverse operations to solve for the variable.
Now, we need to solve the inequality:
\[ 200 + 25h \leq 500 \]
Step 1: Subtract the base fee of 200 from both sides to isolate the term with \(h\):
\[ 25h \leq 500 - 200 \]
\[ 25h \leq 300 \]
Step 2: Divide both sides by 25 to solve for \(h\):
\[ h \leq \frac{300}{25} \]
\[ h \leq 12 \]
This means that Maria can rent the hall for at most 12 hours without exceeding her budget of $500.
Explanation in Context: In the context of the situation, this solution indicates that if Maria wants to stay within her budget for the party hall rental, she can afford to rent the hall for a maximum of 12 hours. If she rents it for any more than 12 hours, her total cost will exceed her budget of $500.
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