Lillian is making chocolate cupcakes to sell at a fundraiser. She only has 3 cups of sugar at home. She goes to the store and buys 2 bags of sugar. Each bag of sugar contains 6 cups. The batter uses 1 cup of sugar per 12 cupcakes. She needs 2 cups of sugar to make enough frosting for a dozen cupcakes. How many dozen cupcakes can she bake and ice with the sugar she has?
Give me a solution to this problem