. The history club wants to spend at most $106.70 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room?

Question

To rent a certain meeting room, a college charges a reservation fee of $32 and an additional fee of $8.30 per hour. The history club wants to spend at most $106.70 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, then solve the Inequality for t.

Answer 1

Cost = $32 + $8.30t          ["$32 and an additional fee of $8.30 per hour"]

 

and

 

Cost ≤ $106.70

 

Substitute value from equation into inequality:

   $32 + $8.30t  ≤  $106.70

   $8.30t ≤ $74.70      [subtract +$32 from both sided retains sense of inequality]

   t ≤ 9         [divide both sides of inequality by +$8.30 retains sense of inequality]

 

The club may rent the room for any number of hours between 0 and 9: 

     0 ≤ t ≤ 9

Answer 2

106.70 = $32 + $8.30T

 

9 = T