Question

to rent a certain meeting room, a college charges a reservation fee of $15 and an additional fee of $4 per hour. the chemistry club wants to spend less than $35 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 inequality

The total cost $C$ of renting the room is the sum of the reservation fee and the hourly fee. The reservation fee is $15$ and the hourly fee is $4$ per hour. So, $C = 15+4t$. The chemistry club wants to spend less than $35$. So the inequality is $15 + 4t<35$.

Step2: Subtract 15 from both sides

To isolate the term with $t$, subtract 15 from both sides of the inequality: $15+4t - 15<35 - 15$, which simplifies to $4t<20$.

Step3: Divide both sides by 4

Divide both sides of the inequality $4t<20$ by 4 to solve for $t$: $\frac{4t}{4}<\frac{20}{4}$, which gives $t < 5$.

Answer:

$t<5$