Maria wants to rent a hall for a birthday party, and she has a budget of $500 for the rental. The hall charges a base fee of $200 plus an additional $25 per hour. Write an inequality to represent this situation, where h

Question

is the number of hours Maria can rent the hall without exceeding her budget. Then, solve the inequality to find the maximum number of hours Maria can afford to rent the hall.
Question 1
Part 1: Write the two-step inequality that represents this situation. Remember, she can AT MOST, spend $500.(2 points)

The base fee is $200, and for each additional hour, she would need to pay $25. so the total cost of renting the hall for h hours can be represented by the inequality:200 + 25h ≤ 500 This inequality states that the total cost of renting the hall, which includes the base fee of $200 and the additional cost of $25 per hour, should not exceed Maria's budget of $500.

68Word(s)68 words written
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. EXPLAIN what your solution means in the context of the situation!

Answer 1

To solve the inequality \(200 + 25h \leq 500\), we will follow these steps:

Step 1: Subtract the base fee from both sides

We start with the inequality: \[ 200 + 25h \leq 500 \]

To isolate the term with \(h\), subtract 200 from both sides: \[ 25h \leq 500 - 200 \] \[ 25h \leq 300 \]

Step 2: Divide by the cost per hour

Next, we divide both sides by 25 to solve for \(h\): \[ h \leq \frac{300}{25} \] \[ h \leq 12 \]

Conclusion

The solution to the inequality is \(h \leq 12\).

In context, this means that Maria can rent the hall for at most 12 hours without exceeding her budget of $500. If she rents the hall for 12 hours, the total cost would be:

\[ \text{Total Cost} = 200 + 25(12) = 200 + 300 = 500 \]

This is exactly her budget. If she rents it for more than 12 hours, she would exceed her budget. Therefore, the maximum number of hours she can afford to rent the hall is 12.