Question

to rent a certain meeting room, a college charges a reservation fee of $32 and an additional fee of $6.10 per hour. the chemistry club wants to spend less than $116.40 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.

Explanation:

Step1: Set up the inequality

The total cost is the reservation fee plus the hourly fee times the number of hours. The reservation fee is $32$, the hourly fee is $6.10$ per hour, and the total cost should be less than $166.40$. So the inequality is $32 + 6.10t<166.40$.

Step2: Subtract 32 from both sides

Subtract 32 from both sides of the inequality: $32 + 6.10t-32<166.40 - 32$. This simplifies to $6.10t<134.40$.

Step3: Divide both sides by 6.10

Divide both sides of the inequality $6.10t<134.40$ by 6.10. We get $t<\frac{134.40}{6.10}$. Since $\frac{134.40}{6.10}=22$.

Answer:

$t < 22$