14% of the registered dogs are pugs, and 11% of the registered dogs are golden retrievers. So (14+11)=25% of the registered dogs are either one or the other.
There are 550 dogs in the club all together, and 25% of them are either pugs or golden retrievers. 25% of 550 is (0.25 • 550) = 137.5 . You can't register half of a dog, so the real number is 137 or 138.