To determine if there is a proportional relationship between the number of days and the total number of pages written, we need to evaluate the ratio of the total number of pages written to the number of days for each data point and see if these ratios are consistent.
Here is the data from the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Number of days} & \text{Total number of pages written} \\
\hline
1 & 10 \\
\hline
2 & 15 \\
\hline
3 & 24 \\
\hline
\end{array}
\][/tex]
We will calculate the ratio of the total number of pages written to the number of days for each entry in the table:
1. On day 1, the ratio is [tex]\(\frac{10 \text{ pages}}{1 \text{ day}} = 10.0\)[/tex].
2. On day 2, the ratio is [tex]\(\frac{15 \text{ pages}}{2 \text{ days}} = 7.5\)[/tex].
3. On day 3, the ratio is [tex]\(\frac{24 \text{ pages}}{3 \text{ days}} = 8.0\)[/tex].
The ratios obtained are: [tex]\(10.0\)[/tex], [tex]\(7.5\)[/tex], and [tex]\(8.0\)[/tex].
A proportional relationship exists if these ratios are the same for all entries. As we can see, the ratios are [tex]\(10.0\)[/tex], [tex]\(7.5\)[/tex], and [tex]\(8.0\)[/tex] which are not equal to each other.
Therefore, we can conclude that there is no proportional relationship between the number of days and the total number of pages written in this case, because the ratios are not consistent.
