Final answer:
Given the proportions in the recipe, each full brownie requires 3/4 cup of sugar. With only one cup of sugar, the greatest number of whole brownies that can be made is 1.
Step-by-step explanation:
To solve the problem, we need to figure out the recipe proportion based on the amount of sugar. If the entire recipe that yields 10 brownies requires 3 1/4 cups of sugar, then each brownie requires 3/4 cup of sugar (3 1/4 cups divided by 10).
Given that we only have one cup of sugar, the greatest number of brownies you can make is simply the amount of sugar available divided by the amount of sugar needed per brownie, which in this case would be 1 divided by 3/4, which yields approximately 1.33 brownies.
However, since we cannot bake a fraction of a brownie, the maximum number of whole brownies we can bake is 1. So, with only one cup of sugar available, the greatest number of brownies you can make is 1.
Learn more about Proportional Reasoning