Suppose you have 34 bread slices and 24 cheese slices. how many cheese sandwiches can you make

17 if you maintain the ratio of 2:1 for bread and cheese, but you would get a remainder of 7 cheese  slices. You could, however, cut up the extra pieces of cheese and add ~0.41 slices of cheese to each sandwich, which would melt into the rest of the cheese if you are grilling the sandwich. Otherwise, it's just an extra chunck, which is perfectly fine.