Answer to Question #318509 in Discrete Mathematics for atoy

Question

there are 450 farmers. 250 pounds of farm beetroot, 110 pounds of farm yams, 75 pounds of farm radish, 45 pounds of farm beetroot and radish, 40 pounds of farm yams and radish, and 30 pounds of farm beetroot and yams Let B, Y, and R represent the farms that grow beets, yams, and radish, respectively.

Determine the number of farmers that farm beetroot, yams, and radish.

Answer 1

Since 250+110+75<450, there are some farmers that grow nothing.

The problem has multiple solutions. Indeed, the following Wienn diagram shows two different solutions: