To find the possible amounts of time the chemistry club could rent the meeting room for, we can set up the inequality based on the given costs.
The total cost for renting the meeting room can be expressed as: \[ \text{Total Cost} = \text{Reservation Fee} + \text{Hourly Rate} \times \text{Number of Hours} \] In this case, the reservation fee is $36, the hourly rate is $6.90, and we need to denote the number of hours rented as \( t \). The inequality representing their budget constraint is: \[ 36 + 6.90t < 98.10 \]
Now we can solve the inequality for \( t \):
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First, subtract the reservation fee from both sides: \[ 6.90t < 98.10 - 36 \] \[ 6.90t < 62.10 \]
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Next, divide both sides by the hourly rate (6.90): \[ t < \frac{62.10}{6.90} \]
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Now, calculate the right side: \[ t < 9 \]
Thus, the possible amounts of time for which the chemistry club could rent the meeting room is: \[ t < 9 \]
This means the club can rent the meeting room for any time less than 9 hours. In other words, they can rent it for any duration from 0 hours up to but not including 9 hours.
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