Even though finding is a key step in arriving at the solution,  is not the final solution. The temptation may be to answer incorrectly with choice . Remember to check that you have answered the question that was asked.

To solve this problem, you must realize that some of the dog owners also own cats and some of the  cat owners also own dogs. This has to be true because is more than ! The question asks how many of the dog owners do not own cats. To solve the problem, first find the number of people who own both a dog and a cat. To do this, let equal the number who own both a dog and a cat. Then . (Note: Adding and  counts twice, so must be subtracted from the sum to get .) Next, the equation can be solved for , yielding . Finally, the number of dog owners who own no cat is .