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.

To find the possible amounts of time for which the Russell family could rent the hall, we need to set up an inequality based on the given information.

Let's assume the number of hours the hall is rented is t.

The reservation fee is $4200.00, and the additional fee per hour is $180.00.

So, the total cost of renting the hall can be calculated as follows:

Total Cost = Reservation Fee + Additional Fee per Hour * Number of Hours
Total Cost = $4200.00 + $180.00 * t

As per the given condition, the Russell family wants to spend at most $5100.00 on renting the hall. So, we can set up the following inequality:

Total Cost <= $5100.00

Substituting the values:

$4200.00 + $180.00 * t <= $5100.00

Now, let's solve this inequality for t by isolating the variable:

$180.00 * t <= $5100.00 - $4200.00
$180.00 * t <= $900.00

Divide both sides of the inequality by $180.00:

t <= $900.00 / $180.00
t <= 5

Therefore, the possible amounts of time for which the Russell family could rent the hall is t <= 5 hours.