Final answer:
To make a casserole that will serve 27 people, you will need 1.125 cups of brown sugar.
Step-by-step explanation:
To find out how much brown sugar is needed to make a casserole that will serve 27 people, we can set up a proportion using the given information. The recipe serves 6 people and calls for 1/4 cup of brown sugar. So, the rate of brown sugar per person is 1/4 cup / 6 people = 1/24 cup per person. To find out how much brown sugar is needed for 27 people, we multiply the rate by the number of people: (1/24 cup/person) * 27 people = 1.125 cups of brown sugar.