## How Many Horses Solution

These types of problems are easy to solve using a diagram like the one below (called a Venn diagram). The blue area represents the horses who ate apples, the red area represents the horses who ate carrots, the overlapping area shows horses who ate both, and the area outside both circles shows horses who ate neither. Since 2 horses ate both, put a “2” in the overlapping area between the red and blue circles. 3 had apples (including the two already in the overlapping part), so one more horse goes in the area that’s just blue. 5 had carrots (including the two in the middle area), so 3 more go in the red area. 4 had neither, so they go outside the circle. Add them all up and you get 10 horses.