Ellen baked 2 dozen cupcakes of which half contained chocolate, two-thirds contained raisins, one-fourth contained chocolate chips, and one-eighth contained nuts. What is the largest possible number of cupcakes that had none of these ingredients?
Here is my attempt at your question:
2 dozen =24 cupcakes. Since 2/3 is the largest fraction, which means: 2/3 x 24 =16 cupcakes that contain raisins. Since 1/2 x 24=12 that contain chocolate, could theoretically be included in the 16 cupcakes that contain raisins, since it does not preclude it! The same reasoning could be applied to the 1/4 x 24 =6 cupcakes that contain chocolate chips could be included in the 16 cupcakes that contain raisins as well. The same goes for the last 1/8 x 24 = 3 cupcakes that contain nuts could also be included in the 16 cupcakes that contain raisins as well!!
So, the conclusion is that the 2/3 x 24=16 could theoretically contain all FOUR ingredients of chocolates, raisins, chocolate chips and nuts. Which means: 24 -16 = 8 Is the largest possible number of cupcakes that have NONE of the 4 ingedients.