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.

Answer 1

You have to make 2 equations

185 = 2(x) + y
X is the hours and y is the setup fee

315 = 4(x) + y

Now you solve the first
185 = 2x+y
185-y = 2x
(185-y)/2 = x
That means you can plug that value into the second equation where you see the x

315 = 4((185-y)/2) + y
315 = 370-2y + y
315 = 370 - y
-55 = - y
55 = y
So y is 55 (the setup fee)

Back to the original

185 = 2(x) + y
185 = 2(x) + 55
130 = 2x
65 = x

Now test it

575 = 8x + y
575 = 8(65) + 55
575 = 520 + 55
575 = 575

Answer 2

The initial setup fee is $55.

The hourly rate is $65.

Explanation:

First of all, we need to find the equation that models this situation.

Let's find the constant ratio of change using two pair of values from the given table.

`m=(575-185)/(8-2)=(390)/(6)=65`

The ratio of change is 65.

In other words, the hourly rate is $65, that is, 65 dollars per hour.

Then, we use the point-slope form to find the equation

`y-y_(1) =m(x-x_(1) )\\y-185=65(x-2)\\y=65x-130+185\\y=65x+55`

Where
`55` refers to the initial condition.

In other words, the initial setup fee is $55.