Real World Situation: Planning a Party

Question

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
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.

*Use the math button below to access inequality symbols!

(2 points)
0 / 10000 Word Limit
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!

*Use the math button below to access inequality symbols!

(2 points)
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:

Given her budget of $500, we can set up the inequality:

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:

Step 1: Subtract the base fee of 200 from both sides to isolate the term with
:

Step 2: Divide both sides by 25 to solve for
:



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.

Answer 1

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:

\[ \text{Total Cost} = \text{Base Fee} + (\text{Hourly Rate} \times \text{Number of Hours}) \]

The base fee is $200, and the hourly rate is $25 per hour. Therefore, her total cost can be expressed as:

\[ \text{Total Cost} = 200 + 25h \]

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.

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 \( h \):

\[ 200 + 25h - 200 \leq 500 - 200 \]

This simplifies to:

\[ 25h \leq 300 \]

Step 2: Divide both sides by 25 to solve for \( h \):

\[ \frac{25h}{25} \leq \frac{300}{25} \]

This simplifies to:

\[ h \leq 12 \]

Explanation in Context:

This means that Maria can rent the hall for at most 12 hours without exceeding her budget of $500. If she rents it for any more than 12 hours, her total cost will exceed her budget. Therefore, if her party lasts up to 12 hours, she can afford to cover the rental cost without any financial issues.