Question

To rent a certain meeting room, a college charges a reservation fee of $45 and an additional fee of $7.80 per hour. The chemistry club wants to spend at most $115.20 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 1

`t\le9`

Step-by-step explanation

Let the number of hours the room is rented be h.

The college charges a reservation fee of $45 and an additional fee of $7.80 per hour.

The expression that represents these charges is:

`45+7.80t`

The chemistry club wants to spend at most $115.20. This implies that they want to spend less than or equal to that amount.

In other words, the charges must be less than or equal to $115.20:

`45+7.80t\le115.20`

Solve for t by collecting like terms:

`\begin{gathered} 7.80t\le115.20-45 \\ 7.80t\le70.2 \\ (7.80t)/(7.80)\le(70.2)/(7.80) \\ t\le9 \end{gathered}`

Therefore, they can rent the room for at most 9 hours.