Questions: To rent a certain meeting room, a college charges a reservation fee of 47 and an additional fee of 8.40 per hour. The history club wants to spend less than 89.00 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.

To rent a certain meeting room, a college charges a reservation fee of 47 and an additional fee of 8.40 per hour. The history club wants to spend less than 89.00 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.

Transcript text: To rent a certain meeting room, a college charges a reservation fee of $47 and an additional fee of $8.40 per hour. The history club wants to spend less than $89.00 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 $t$.

Solution

Solution Steps

Step 1: Formulate the Inequality

Given the problem statement, we can formulate the inequality as follows: $$R + Pt \leq M$$ where:

$R$ is the reservation fee, which is a fixed cost of $47$.
$P$ is the price per hour, a variable cost of $8.4$ per hour.
$M$ is the maximum budget, set at $89$.
$t$ represents the possible rental time in hours.

Step 2: Solve the Inequality for $t$

To find the possible rental times that meet the budget constraint, we solve the inequality for $t$:

Subtract $R$ from both sides to isolate terms involving $t$: $$Pt \leq M - R$$
Divide both sides by $P$ to solve for $t$: $$t \leq \frac{{M - R}}{{P}}$$ Substituting the given values, we get: $$t \leq \frac{89 - 47}{8.4}$$ $$t \leq 5$$