To represent Maria's situation with an inequality, we can start by expressing the total cost of renting the hall. The total cost consists of a base fee of $200 plus an additional $25 for each hour she rents the hall.
We can write the cost \( C \) as: \[ C = 200 + 25h \]
Since Maria has a budget of at most $500, we set up the inequality: \[ 200 + 25h \leq 500 \]
This inequality represents the situation where Maria wants the total cost to be less than or equal to her budget of $500.
So the two-step inequality is:
\[ 200 + 25h \leq 500 \]
Now, let's move on to Part 2, where we will solve the inequality to find the maximum number of hours Maria can afford to rent the hall.
Next Steps for Part 2:
-
Subtract 200 from both sides: \[ 25h \leq 500 - 200 \] \[ 25h \leq 300 \]
-
Now, divide both sides by 25: \[ h \leq \frac{300}{25} \] \[ h \leq 12 \]
Conclusion:
The maximum number of hours Maria can afford to rent the hall is 12 hours.