Problem 17 (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. Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cookies? (Some eggs and some cookies may be left over.)