Question

to rent a certain meeting room, a college charges a reservation fee of $16 and an additional fee of $a per hour for renting the room. what are the possible numbers of hours the chemistry club could rent the meeting room? the chemistry club wants to spend at most $amount not visible. write your answer as an inequality solved for t. use t for the number of hours.

Explanation:

Step1: Set up the cost - inequality

The total cost of renting the room is the reservation fee plus the per - hour fee times the number of hours. The reservation fee is $16$ and the per - hour fee is $4$. Let $t$ be the number of hours. The chemistry club wants to spend at most $50$. So the inequality is $16 + 4t\leqslant50$.

Step2: Subtract 16 from both sides

To isolate the term with $t$, we subtract 16 from both sides of the inequality: $16+4t - 16\leqslant50 - 16$. This simplifies to $4t\leqslant34$.

Step3: Divide both sides by 4

Dividing both sides of the inequality $4t\leqslant34$ by 4 gives $t\leqslant\frac{34}{4}=8.5$. Since $t$ represents the number of hours, and it cannot be negative, the possible values of $t$ satisfy $0\leqslant t\leqslant8.5$.

Answer:

$0\leqslant t\leqslant8.5$