Question

to rent a certain meeting room, a college charges a reservation fee of $17 and an additional fee of $6 per hour. the chemistry club wants to spend at most $59 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 is the sum of the reservation fee and the hourly fee. The reservation fee is $17$ and the hourly fee is $6$ per hour. So, $C = 17+6t$. The club wants to spend at most $59$, so $17 + 6t\leqslant59$.

Step2: Solve the inequality for $t$

Subtract $17$ from both sides of the inequality: $17+6t - 17\leqslant59 - 17$, which simplifies to $6t\leqslant42$.

Step3: Isolate $t$

Divide both sides of the inequality $6t\leqslant42$ by $6$: $\frac{6t}{6}\leqslant\frac{42}{6}$, so $t\leqslant7$.

Answer:

$t\leqslant7$