please help! question is below

Question

To rent a certain meeting room, a college charges a reservation fee of $37 and an additional fee of $6.60 per hour. The chemistry club wants to spend less than $89.80 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 inequality for t
.

Answer 1

6.6(t) + 37 < 89.80                                Set up the equation

6.6(t) < 52.80                                       Subtract 37 from both sides

t < 8                                                    Divide both sides by 6.6

0 < t < 8                                              This is the general answer

However, using the idea that the room is rented in 1 hour increments (no fractional time), then 1 hour would be the least amount of time and 7 hours would be the greatest amount of time given the constraints of the problem.

1 <= t <= 7 For t in 1 hour increments

Answer 2

Honor, let's look at this.  I'm assuming you have some choices once you figure out the problem.

 

Let's say they rented the room for 2 hours.  Then, they paid $37 plus $13.20, because $6.60(2) = $13.20, so they paid $50.20 altogether.

 

If t = the number of hours, then for t hours, they pay $37 + $6.60t.  Since they want to pay less than $89.80, then we have to set up an inequality.

 

37 + 6.60t < 89.80.  We solve it just like a regular equation.

 

6.60t < 52.80

       t < 8

 

Any of your choices less than 8 are an answer.  8 itself would not work, as they would not be spending LESS than $89.80.