Problem 19 (1999 AMC 8)

At Central Middle School the $108$ students who take the AMC8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of $15$ cookies, lists these items: $1.5$ cups flour, $2$ eggs, $3$ tablespoons butter, $3/4$ cups sugar, and $1$ package of chocolate drops. They will make only full recipes, not partial recipes. The drummer gets sick. The concert is cancelled. Walter and Gretel must make enough pans of cookies to supply $216$ cookies. There are $8$ tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may be left over, of course.)