Ratios Guest at the party are seated at three tables the small table has five seats and two pizzas the medium table has seven seats and three pizzas the large table has twelve seats and has five pizza?

At each table the Pizza will be sliced into only enough slices to make equal shares for that table... We'll be working with circular pizza - each one being 360º around

So that the table with 5 seats and two pizzas can cut each pizza into angles of 144 degrees and give four people one slice and the last person gets two half-sized sliced of 72 degrees..... (144 x 4) + (72 x 2) = 720 (= 360 x 2)

The table with 7 pizzas can slice their three pizzas into angles of 154 degrees. That way six people each get 1 slice and the last person gets three pieces of 52 degrees - which add up to to 156 degrees and makes up for the fact that they don't get a proper slice.

(6 x 154) + 156 = 1080 (= 360 x 3)

The table with 12 people can divide each pizza into 150 degree angles and that way 10 people get one slice each and two people can then get two slices of 60 degrees and one of 30 degrees

(10 x 150) + 2((2 x 60) +30) = 1800 (= 360 x 5)

So the folks at the medium table get slightly more than the others and one of them gets a bit more than the rest, unless they have an incredibly accurate mathematician doing the cutting of the pizzas.

Of course the obvious thing to do is to cut the pizzas before they get to the tables at all.... cut them in the kitchen and that way 10 pizzas can be divided between (5 + 7 + 12) 24 people by giving each one five pieces of 30 degree angles..... and that way there'd be fewer arguments about the toppings!