Dave's sister baked $3$ dozen pies of which half contained chocolate, two thirds contained marshmallows, three-fourths contained cayenne, and one-sixths contained salted soy nuts.  What is the largest possible number of pies that had none of these ingredients?
So the total number of pies is $3$ dozen, or $3*12=36$ pies. That would be $3/4$ of the pies, or $3/4*36=27$ pies. So the largest number of pies that could have none of the ingredients is $36-27=9$ pies.

