Question

Please I Need Help 20pts

To rent a certain meeting room, a college charges a reservation fee of $39 and an additional fee of $9.80 per hour. The math club wants to spend at most $117.40 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

8 is the very maximum number of hours the room can be rented. As long as 8 is not exceeded, the room is rentable for what money the math club has.

Explanation:

Givens

• Maximum payment = 117.40
• Cost per hour = 9.80
• Fixed charge = 39 dollars

Formula

payment ≥ 39 + 9.80*t where t is in hours.

Solution

117.40 ≥ 39 + 9.80*t Subtract 39 from both sides.

117.40 - 39 ≥9.80*t

78.40 ≥ 9.80*t Divide by 9.8

78.40/9.80 ≥ 9.80*t/9.80

8 ≥ t

Answer t≥ 8

Answer 2

0 < t ≤ 8 (in hours)

Up to (and including) 8 hours

Explanation:

Let t = number of hours the room is rented

Given:

• Reservation fee = $39
• Fee per hour = $9.80
• Maximum total cost = $117.40

Create an equation using the given information and solve for t:

⇒ 39 + 9.8t ≤ 117.4

Subtract 39 from both sides:

⇒ 9.8t ≤ 78.4

Divide both sides by 9.8

⇒ t ≤ 8

Therefore, the possible amounts of time for which they could rent the meeting room is 0 < t ≤ 8 (in hours)