Final answer:
The red sugar has a proportional relationship with the number of cookies, as its ratio of tsp per cookie remains consistent when the number of cookies doubles.
Step-by-step explanation:
The question asks which color of sugar has a proportional relationship with the number of cookies decorated. A proportional relationship means that as the number of cookies doubles, the amount of sugar used should also double. To find the proportional relationship, we need to compare the teaspoon amounts for each color of sugar with the number of cookies they decorate.
For a proportional relationship to exist between the two variables (in this case, teaspoons of sugar and number of cookies), the ratio of teaspoons of sugar per cookie should be the same, regardless of the number of cookies. We will compare the amounts for 12 cookies and 24 cookies for each color of sugar:
Blue sugar: 14 tsp for 12 cookies, 28 tsp for 24 cookies (28/24 = 14/12 = 7/6)
Green sugar: 3 tsp for 12 cookies, 6 tsp for 24 cookies (6/24 = 3/12 = 1/4)
Purple sugar: 1 tsp for 12 cookies, 2 tsp for 24 cookies (2/24 = 1/12 = 1/12)
Red sugar: 12 tsp for 12 cookies, 24 tsp for 24 cookies (24/24 = 12/12 = 1)
From this, we can see that the red sugar shows a consistent ratio of 1 tsp per cookie, whether there are 12 or 24 cookies. This indicates that red sugar has a proportional relationship between the teaspoons of sugar used and the number of cookies decorated.