The Big Thanksgiving Dinner

A large banquet served between 500 and 600 people. The dinner rolls came in baker's dozen (packages of 13). After everyone had been served a roll, there were a number of empty packages plus one open package with 10 rolls left. The pies served for desert had each been cut into ninths, and after everyone had been served a slice there were a number of empty pie tins plus one pie with 4 slices left. The tables in the banquet hall each had room for 15 guests. All but one of the tables were full.

How many people attended the banquet?

How many people were seated at the table that was not full?

How many pies were there? How many packages of rolls?

Hint: Write an algebraic expression for how many rolls were eaten, and another one for how many pie slices were eaten. Only one possible result between 500 and 600 will satisfy both.

Any help would be greatly appreciated! Thanks!