Question

to rent a certain meeting room, a college charges a reservation fee of $45 and an additional fee of $7.40 per hour. the chemistry club wants to spend less than $74.60 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 of renting the meeting - room is the reservation fee plus the hourly fee times the number of hours. The reservation fee is $45$ and the hourly fee is $7.40$ per hour. The club wants to spend less than $74.60$. So the inequality is $45 + 7.4t<74.60$.

Step2: Subtract 45 from both sides

To isolate the term with $t$, we subtract 45 from both sides of the inequality:
$45 + 7.4t-45<74.60 - 45$
$7.4t<29.6$

Step3: Divide both sides by 7.4

To solve for $t$, we divide both sides of the inequality by 7.4:
$\frac{7.4t}{7.4}<\frac{29.6}{7.4}$
$t < 4$

Answer:

$t<4$