Question

To rent a certain meeting room, a college charges a reservation for of $14 and an additional fee of $6 per hour. The chemistry club wants to spend less than $86 on renting the room. What are the possible numbers the chemistry club could rent the meeting room? (Use t for number of hours)

Answer 1

the chemistry club can rent the meeting room for any number of hours between 1 and 11 (inclusive) and stay within their budget of $86.

Explanation:

Let's first set up an equation to represent the situation:

Total cost = Reservation fee + Hourly fee = $14 + $6t

The problem states that the chemistry club wants to spend less than $86 on renting the room, so we can set up an inequality:

$14 + $6t < $86

Simplifying this inequality, we get:

$6t < $72

Dividing both sides by 6, we get:

t < 12

So the number of hours the chemistry club can rent the room is less than 12. To find the possible integer values of t, we need to consider that t must be a positive integer since you cannot rent a room for a negative or fractional number of hours. We also need to consider that the total cost must be less than $86, so we can set up the following inequality:

$14 + $6t ≤ $86

Simplifying this inequality, we get:

$6t ≤ $72

Dividing both sides by 6, we get:

t ≤ 12

Therefore, the possible integer values of t are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.

So, the chemistry club can rent the meeting room for any number of hours between 1 and 11 (inclusive) and stay within their budget of $86.