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To rent a certain meeting room a college charges a reservation fee of $43 an additional fee of $8.70 per hour. The history club wants to spend at most $77.80 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 in equality for t.

Answer :

We have an initial value of $43 and every hour the price of the reservation increases $8.70, then, the function that determinates the price for the meeting room is

[tex]P(t)=43+8.7t[/tex]

The history club have a limit value that is $77.80, then, to find the amount of hours they can spend at the meeting room we just need to solve the following inequality:

[tex]77.8\ge43+8.7t[/tex]

Solving for t:

[tex]\begin{gathered} 77.8\ge43+8.7t \\ 34.8\ge8.7t \\ 4\ge t \end{gathered}[/tex]

The maximum amount of hours they can spend in the meeting room is 4 hours.

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