Question

to rent a certain meeting room, a college charges a reservation fee of $13 and an additional fee of $5 per hour. the chemistry club wants to spend at most on renting the room. what are the possible numbers of hours the chemistry club could rent the meeting room? use t for the number of hours. write your answer as an inequality solved for t.

Explanation:

Step1: Set up the cost - function

The total cost $C$ of renting the meeting room is the sum of the reservation fee and the hourly fee. The reservation fee is $13$ and the hourly fee is $5$ per hour. So, $C = 13+5t$. Let's assume the chemistry club has a maximum amount of money $M$ to spend. Since the problem doesn't state an upper - bound on spending, we'll assume they want to spend at most some amount. Let's say they have a budget, and the total cost $C$ should satisfy the inequality $13 + 5t\leq M$. If we assume they want to spend all their available money (or less), and we want to find the possible values of $t$ in terms of the cost structure only, we can assume they have some non - negative amount to spend. Let's assume they want to spend as much as possible within their means. If we assume they have a budget of $M$ dollars, we have the inequality $13+5t\leq M$. If we assume they want to find the general case for the number of hours they can rent given their cost structure, and we assume they can't spend more than they have, we can rewrite the inequality for $t$. First, we isolate the term with $t$:
$5t\leq M - 13$.

Step2: Solve for $t$

Divide both sides of the inequality $5t\leq M - 13$ by $5$ (since $5>0$, the direction of the inequality sign remains the same). We get $t\leq\frac{M - 13}{5}$. If we assume they have no upper - bound on spending in a practical sense (i.e., they can spend as much as they want), and we just consider the non - negativity of the number of hours and the cost structure, and we assume they want to find the maximum number of hours they can rent given their cost structure, we can also assume they want to spend all their available money. If we assume they have a budget of $M$ dollars, and we want to find the general form of the inequality for $t$. Since the cost $C=13 + 5t$ and we assume they can spend as much as they want (but not more than they have), we have $t\geq0$ (because the number of hours can't be negative). Also, if we assume they have a budget of $M$ dollars, $t\leq\frac{M - 13}{5}$. In the most general non - budget - specified case, if we just consider the cost structure and non - negativity of hours, we assume they can spend as much as they want (within reason), and we get $t\geq0$.

Answer:

$t\geq0$