Question

In a class of 29 children, each of 20 children has a dog and each of 15 has a cat. How many of the children have both a dog an a cat

using Vinn Diagrams

Answer 1

Your Venn diagram will consist of 2 intersections circles, C for cats, and D for dogs.
Place x in the intersection of the two circles
Place 20-x in the part of D not overlapping
Place 15-x in the part of C not overlapping

then 20-x + x + 15-x = 29
-x = -6
x = 6

so 6 children have both a dog and a cat.