To determine if the data is proportional, we need to compare the ratios of the number of scouts in the troop to the cases sold for each data point given in the table.
Here are the steps to do that:
1. Calculate the ratio for each given pair:
- For the first pair (4 scouts, 0.5 cases):
[tex]\[
\text{Ratio} = \frac{\text{Cases Sold}}{\text{Number of Scouts}} = \frac{0.5}{4} = 0.125
\][/tex]
- For the second pair (16 scouts, 2 cases):
[tex]\[
\text{Ratio} = \frac{\text{Cases Sold}}{\text{Number of Scouts}} = \frac{2}{16} = \frac{2}{16} = 0.125
\][/tex]
- For the third pair (20 scouts, 2.5 cases):
[tex]\[
\text{Ratio} = \frac{\text{Cases Sold}}{\text{Number of Scouts}} = \frac{2.5}{20} = 0.125
\][/tex]
2. Compare the ratios:
The ratios we have calculated are:
[tex]\[
0.125, \, 0.125, \, 0.125
\][/tex]
3. Determine if the ratios are equivalent:
Since all the ratios are equal (0.125), the data sets indicate that the ratios of cases sold to the number of scouts are constant.
4. Conclusion:
Since the ratios of cases sold to the number of scouts in the troop are equivalent for all given data points, it indicates that the cookie sales by the scout troop are in a proportional relationship.
Thus, the data is proportional.
