Question

to rent a certain meeting room, a college charges a reservation fee of $17 and an additional fee of $5 per hour. the chemistry club wants to spend less than $52 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 - equation

The total cost $C$ of renting the room for $t$ hours is the sum of the reservation fee and the per - hour fee. The reservation fee is $17$ and the per - hour fee is $5$ per hour. So, $C = 17+5t$.

Step2: Set up the inequality

The chemistry club wants to spend less than $52$. So, we set up the inequality $17 + 5t<52$.

Step3: Solve the inequality for $t$

Subtract $17$ from both sides: $17+5t - 17<52 - 17$, which simplifies to $5t<35$.
Then divide both sides by $5$: $\frac{5t}{5}<\frac{35}{5}$, resulting in $t < 7$.

Answer:

$t<7$