Question

to rent a certain meeting room, a college charges a reservation fee of $43 and an additional fee of $5.30 per hour. the chemistry club wants to spend less than $85.40 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. The reservation fee is $43$ and the hourly fee is $5.30t$. The total cost must be less than $85.40$. So the inequality is $43 + 5.30t<85.40$.

Step2: Subtract 43 from both sides

Subtract 43 from both sides of the inequality:
$$43 + 5.30t-43<85.40 - 43$$
$$5.30t<42.4$$

Step3: Divide both sides by 5.30

Divide both sides of the inequality by 5.30:
$$t<\frac{42.4}{5.30}$$
$$t < 8$$

Answer:

$t < 8$