Question

To rent a certain meeting room, a college charges a reservation fee of
$36
and an additional fee of
$6.60
per hour. The chemistry club wants to spend less than
$88.80
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

@mathstudent55

Answer 2

room rental = fixed cost + hourly cost

ok so far?

Answer 3

yes

Answer 4

The fixed cost is the reservation fee, so we can replace "fixed cost" with 36 to get

room rental = 36 + hourly fee

still ok?

Answer 5

ok

Answer 6

The hourly fee is $6.60/hour
If an hour costs $6.60, what do t hours cost?

Answer 7

t*6.60

Answer 8

Correct.
We can write it simply as 6.6t

Answer 9

ok

Answer 10

Now we have the following cost expression:

total cost = 36 + 6.6t

Ok?

Answer 11

ok

Answer 12

They want to spend less than $88.
We set our cost expression less than 88 to get our inequality.

36 + 6.6t < 88

Answer 13

How do we know we use < and not \(\le\)?

The problem tells us they want to spend LESS than $88. That means the cost must be less than $88, and < means less than.

If the problem stated they want to spend AT MOST $88, then they could spend $88 or less, and $88 would have to be included, then you'd use \(\le\).

Ok?

Answer 14

ok

Answer 15

The next step is to solve the inequality.

Answer 16

ok....36 + 6.6t < 88
t <7.87878787

Answer 17

36 + 6.6t < 88

6.6t < 52

t < 7.8787...

You are correct.

If they need to rent it for a whole number of hours, then they can rent it for less than 8 hours.