Question

What equation models the data in the table if d = number of days and c = cost?


Days Cost
2 44
3 66
5 110
6 132








d = 22c


c = d + 22d


c = 22d


c = d + 22

Answer 1

To find the correct equation that models the data in the table, we will look for a relationship between the number of days \( d \) and the cost \( c \).

Let's analyze the data provided:

- For \( d = 2 \), \( c = 44 \)
- For \( d = 3 \), \( c = 66 \)
- For \( d = 5 \), \( c = 110 \)
- For \( d = 6 \), \( c = 132 \)

Now, let's see if we can find a pattern in the costs in relation to the days.

1. Find the cost per day for the days given:

- For \( d = 2 \): \( \frac{44}{2} = 22 \)
- For \( d = 3 \): \( \frac{66}{3} = 22 \)
- For \( d = 5 \): \( \frac{110}{5} = 22 \)
- For \( d = 6 \): \( \frac{132}{6} = 22 \)

From this analysis, we can see that the cost \( c \) is consistently \( 22 \) multiplied by the number of days \( d \). Therefore, we can express the relationship as:

\[ c = 22d \]

Now let's compare this to the answer options provided:

- \( d = 22c \) (not correct)
- \( c = d + 22d \) (not correct)
- \( c = 22d \) (correct)
- \( c = d + 22 \) (not correct)

The correct equation that models the data is:

**\( c = 22d \)**