Question

The table below shows the cost at a popular cruise with a minimum for 4 days.
Number of Days. cost($)
4. 910.
5. 1075.
6. 1240.

the cost per day is $____.
the initial cost is $______.

Answer 1

To determine the cost per day and the initial cost (fixed cost), let's analyze the data provided.

We can set up the cost as a linear function of the number of days. From the table, we have the following costs for different numbers of days:

- For 4 days: $910
- For 5 days: $1075
- For 6 days: $1240

### To find the cost per day:

1. Calculate the difference in cost as we increase the number of days:
- From 4 to 5 days:
\[
1075 - 910 = 165\
\]
- From 5 to 6 days:
\[
1240 - 1075 = 165
\]

The cost per day is consistent and is $165.

### To find the initial cost:

We can use the cost for 4 days to find an initial cost (fixed cost). Assuming \( C \) is the total cost, \( m \) is the cost per day, and \( b \) is the initial cost:

Using the formula:
\[
C = b + m \cdot d
\]

Substituting for 4 days:
\[
910 = b + 165 \cdot 4
\]

Calculating \( 165 \cdot 4 \):
\[
165 \cdot 4 = 660
\]

So:
\[
910 = b + 660
\]

To solve for \( b \):
\[
b = 910 - 660 = 250
\]

### Final answers:

- The cost per day is **$165**.
- The initial cost is **$250**.