To rent a certain banquet hall, there is a reservation fee of $4200.00 and an additional fee of $180.00 per hour. The Russell family wants to spend at most $5100.00 on renting the hall.
What are the possible amounts of time for which they could rent the hall? Use t for the number of hours the hall is rented, and solve your inequality for t.
solve
180t + 4200 ≤ 5100
I got
Let t = number of hours hall is rented
then 180t + 4200 <= 5100
.
Solving for t:
180t <= 900
t <= 5 hours
correct
To find the possible amounts of time for which the Russell family could rent the hall, we need to consider the total cost of renting the hall.
The reservation fee is a fixed amount of $4200.00. Along with that, there is an additional fee of $180.00 per hour.
Let's assume the number of hours the hall is rented as 't'.
So, the total cost of renting the hall for 't' hours can be calculated using the equation:
Cost = Reservation fee + (Hourly rate * Number of hours)
Cost = $4200.00 + ($180.00 * t)
The Russell family wants to spend at most $5100.00 on renting the hall. Therefore, we can set up the following inequality to represent this:
$4200.00 + ($180.00 * t) ≤ $5100.00
To solve this inequality for 't', we can follow these steps:
Step 1: Subtract $4200.00 from both sides of the inequality:
($180.00 * t) ≤ $5100.00 - $4200.00
($180.00 * t) ≤ $900.00
Step 2: Divide both sides of the inequality by $180.00 to isolate 't':
t ≤ $900.00 / $180.00
t ≤ 5
Therefore, the possible amounts of time for which the Russell family could rent the hall are any values of 't' that are less than or equal to 5. In other words, they can rent the hall for up to 5 hours.