You would need about 34 2/3 tablespoons of butter. Convert the fraction into an improper fraction, so 8/3. Then multiply that by 13 (you and your brother are included in the 15 people I suppose) and you get 104/3. Simplify that to get a mixed number and you have 34 2/3.
If you use 2 2/3 tablespoons for you and your brother, that means, you need 2 2/3 tablespoons for two servings, how many tablespoons for 15 servings then?