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Question

Kiki wants to rent a bounce house for her daughter's party. The cost, y, to rent a bounce house for a number of hours, x, is shown in the table. The initial set-up fee is included in the cost.
Hours (x) Cost (y)
2 $185
4 $315
6 $445
8 $575

To rent a bounce house, the initial setup fee is $
, and the hourly rate is $
.

Answer 1

To find the initial setup fee and the hourly rate, we can analyze the table provided.

1. First, let's identify the cost for different hours:

   • For 2 hours: $185
   • For 4 hours: $315
   • For 6 hours: $445
   • For 8 hours: $575

2. Now, calculate the increase in cost as the hours increase.

   • From 2 to 4 hours: $315 - $185 = $130 (for 2 additional hours)
   • From 4 to 6 hours: $445 - $315 = $130 (for 2 additional hours)
   • From 6 to 8 hours: $575 - $445 = $130 (for 2 additional hours)

This shows that the cost increases by $130 for each additional 2 hours, which means the hourly rate is:

\[ \text{Hourly Rate} = \frac{130}{2} = 65 \]

3. To find the initial setup fee, we can use the cost equation with the number of hours. Letting \( C \) be the cost, \( h \) be the hourly rate, and \( f \) be the initial setup fee:

\[ C = f + (h \cdot x) \]

Using the first data point (2 hours, $185):

\[ 185 = f + (65 \cdot 2) \] \[ 185 = f + 130 \] \[ f = 185 - 130 = 55 \]

Now, we have found:

• Initial setup fee (f) = 55
• Hourly rate (h) = 65

So, the answers are:

Initial setup fee: 55
Hourly rate: 65