Question

24.
What equation models the data in the table if d = number of days and c = cost?


Days Cost
2 6
3 9
5 15
6 18








c = d + 3


c = 3d


c = d + 3d


d = 3c

Answer 1

To determine which equation models the data in the table, we can look at how the cost (c) changes with the number of days (d).

Here’s the given data:

- For d = 2, c = 6
- For d = 3, c = 9
- For d = 5, c = 15
- For d = 6, c = 18

Let's analyze the relationship:

1. **Calculate cost per day**:
- From d = 2 to c = 6: \( \frac{6}{2} = 3 \)
- From d = 3 to c = 9: \( \frac{9}{3} = 3 \)
- From d = 5 to c = 15: \( \frac{15}{5} = 3 \)
- From d = 6 to c = 18: \( \frac{18}{6} = 3 \)

The cost increases by 3 for every day, suggesting a linear relationship where the cost is three times the number of days.

Therefore, the equation can be expressed as:

\[
c = 3d
\]

Now let's verify with each point:

- For d = 2: \( c = 3 \times 2 = 6 \) (correct)
- For d = 3: \( c = 3 \times 3 = 9 \) (correct)
- For d = 5: \( c = 3 \times 5 = 15 \) (correct)
- For d = 6: \( c = 3 \times 6 = 18 \) (correct)

Thus, the equation that models the data in the table is:

\[
\boxed{c = 3d}
\]