Question

The table below shows the cost at a resort with a minimum stay of 2 days.
number of days cost($)
2. 395.
3. 520
4. 645.

The cost per day is $___.
The initial cost $_____.

Answer 1

To find the cost per day and the initial cost, we can analyze the information provided in your table.

1. **Cost per day**: We can see the costs for different numbers of days and calculate the cost per day.

- For 2 days, the cost is $395. Therefore, the cost per day is:
\[
\text{Cost per day} = \frac{395}{2} = 197.50
\]

- For 3 days, the cost is $520. Therefore, the cost per day is:
\[
\text{Cost per day} = \frac{520}{3} \approx 173.33
\]

- For 4 days, the cost is $645. Therefore, the cost per day is:
\[
\text{Cost per day} = \frac{645}{4} = 161.25
\]

Since the cost per day seems to decrease as the number of days increases, we should note that the initial cost likely includes some base fee for the minimum stay.

2. **Initial cost**: We can find the base cost (initial cost) by determining the fixed part of the cost.

- Using the information for 2 days ($395), we can calculate the base cost as follows:

Let \( C \) be the initial cost, and \( p \) be the cost per additional day after the minimum two days. We can write the equation for the cost:

\[
C + 2p = 395
\]
Now, we try using the 3 days:

\[
C + 3p = 520
\]

We have a system of equations:
1. \( C + 2p = 395 \) (1)
2. \( C + 3p = 520 \) (2)

Subtract equation (1) from equation (2):

\[
(C + 3p) - (C + 2p) = 520 - 395
\]
\[
p = 125
\]

Now substitute \( p \) back into equation (1) to find \( C \):
\[
C + 2(125) = 395
\]
\[
C + 250 = 395
\]
\[
C = 395 - 250 = 145
\]

Thus, the initial cost is $145.

To summarize:
- The cost per day (for an additional day) is $125 after the initial cost for the minimum stay.
- The initial cost is $145.

Final Answer: The cost per day is $125, and the initial cost is $145.