Question

Mary wants to rent a hall for a party and she has a budget of $500 for the rental. The hall charges a fee of $200 plus $25 per hour Write an inequality to represent the situation where h is the number of hours mary can rent the hall without exceeding her budget. Then solve to find the maximum number of hours she can afford to rent the hall

Answer 1

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 \( h \):

1. Subtract 200 from both sides:

\[
25h \leq 500 - 200
\]

\[
25h \leq 300
\]

2. 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**.