Question

Number of nights- 0, 2, 4, 6
Total coast- 55, 385, 717, 1045

Nightly charge?

How much is the cleaning fee?

Write an equation y=total cost X=number of nights-

How much to stay 1 week?

Answer 1

To determine the nightly charge and the cleaning fee, we can analyze the data you've given.

Let's set up the variables:

- Let \( x \) be the number of nights.
- Let \( y \) be the total cost.

From your data:

\( \begin{align*}
\text{When } x = 0, & \quad y = 55 \\
\text{When } x = 2, & \quad y = 385 \\
\text{When } x = 4, & \quad y = 717 \\
\text{When } x = 6, & \quad y = 1045 \\
\end{align*} \)

The first observation is that when \( x = 0 \), the total cost is \( 55 \). This suggests that there is a base cleaning fee of \( 55 \) when no nights are booked.

Next, we'll find the nightly charge, \( n \).

We can use the data points (excluding the \( x = 0 \) point) to determine the cost per night.

From the points:

1. For \( x = 2 \), we have the equation:
\[
y = 55 + 2n \rightarrow 385 = 55 + 2n \implies 2n = 385 - 55 = 330 \implies n = \frac{330}{2} = 165
\]

2. We can confirm this by using another set of points:
- For \( x = 4 \):
\[
y = 55 + 4n \rightarrow 717 = 55 + 4n \implies 4n = 717 - 55 = 662 \implies n = \frac{662}{4} = 165.5 \text{ (not consistent)}
\]

- For \( x = 6 \):
\[
y = 55 + 6n \rightarrow 1045 = 55 + 6n \implies 6n = 1045 - 55 = 990 \implies n = \frac{990}{6} = 165
\]

From the equations, we have confirmed that our value of the nightly charge \( n = 165 \).

## Summary:
- Nightly charge \( n = 165 \)
- Cleaning fee \( = 55 \)

### Final Equation
The equation representing the total cost \( y \) based on the number of nights \( x \) is:
\[
y = 55 + 165x
\]

### Cost for 1 Week (7 Nights)
To find the total cost for staying 1 week (7 nights):

\[
y = 55 + 165 \times 7
\]
\[
y = 55 + 1155 = 1210
\]

So, the total cost to stay for 1 week (7 nights) is **$1210**.