thou theprese 35 Shyan Solving a decinal word probiom uning a twoutep linear inecquelity Sly To rent a certain meeting room, a college charges a reservation fee of \( \$ 48 \) and an additional fee of \( \$ 5.30 \) per hour. The film club wants to spend at most \( \$ 95.70 \) on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use \( t \) for the number of hours the meeting room is rented, and solve your inequality for \( t \). \( \square \) \( <\square \) \( \square>C \)

To set up the inequality for the film club's budget, we first account for the fixed reservation fee and the hourly rate. The total cost can be expressed as: \[ \text{Total Cost} = 48 + 5.30t \] To stay within their budget, we create the inequality: \[ 48 + 5.30t \leq 95.70 \] Now, subtract \( 48 \) from both sides: \[ 5.30t \leq 47.70 \] Next, divide by \( 5.30 \): \[ t \leq \frac{47.70}{5.30} \] Calculating \( \frac{47.70}{5.30} \) gives us approximately \( 9 \). Therefore, the film club can rent the meeting room for a maximum of \( 9 \) hours. To sum it all up, the possible amounts of time for renting the room can be expressed as: \( t < 9 \) Alternately, if they prefer whole hours, they'll have from \( 0 \) to \( 9 \) hours in total. Renting space is a crucial decision for clubs like film clubs! Consider whether you want to rent at peak times or off-peak times to make the most of your budget. Off-peak hours can often be cheaper, giving you more hours for less money, which is perfect for extended meetings or film screenings! When tackling these types of problems, common mistakes include forgetting to isolate \( t \) correctly or making a calculation error when dividing, especially with decimals. Double-check your arithmetic, and don't hesitate to plug the values back into the original expression to ensure they fit your budget!