to rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $9.70…

to rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $9.70 per hour. the film club wants to spend less than $116.90 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room? use t for the number of hours the meeting room is rented, and solve your inequality for t.

to rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $9.70 per hour. the film club wants to spend less than $116.90 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room? use t for the number of hours the meeting room is rented, and solve your inequality for t.

Answer

Explanation:

Step1: Set up the inequality

The total cost of renting the meeting - room is the reservation fee plus the cost per hour times the number of hours. The reservation fee is $49$ and the cost per hour is $9.70$. The film club wants to spend less than $116.90$. So the inequality is $49 + 9.7t<116.90$.

Step2: Subtract 49 from both sides

To isolate the term with $t$, we subtract 49 from both sides of the inequality: $49 + 9.7t-49<116.90 - 49$. This simplifies to $9.7t<67.9$.

Step3: Divide both sides by 9.7

Dividing both sides of the inequality $9.7t<67.9$ by 9.7 gives us $t < \frac{67.9}{9.7}$. Since $\frac{67.9}{9.7}=7$, the solution is $t < 7$.

Answer:

$t < 7$