Question

to rent a certain meeting room, a college charges a reservation fee of $16 and an additional fee of $6 per hour. the chemistry club wants to spend at most $58 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 - inequality

The reservation fee is $16$ and the additional fee is $6$ per hour. If $t$ is the number of hours, the total cost $C$ is $C = 16+6t$. The club wants to spend at most $58$, so the inequality is $16 + 6t\leqslant58$.

Step2: Subtract 16 from both sides

$16+6t - 16\leqslant58 - 16$, which simplifies to $6t\leqslant42$.

Step3: Divide both sides by 6

$\frac{6t}{6}\leqslant\frac{42}{6}$, so $t\leqslant7$.

Answer:

$t\leqslant7$