So I had to come up with another simple proof. At a store there are cats, dogs, and bears. There are more cats than dogs, and more dogs than bears. Is there a way to prove that the fraction b/(c+d+b) is greater than 1/3? Or less? Or even equal? I reasoned that for b/c+d+b to be less than or equal to 1/3, the number of cats, dogs, and bears must be equal, or cats or dogs must be less than bears. Thus, since cats and dogs have to be greater than bears, b/c+d+b must be greater than 1/3. Is that sound?

EDIT: I just now realised that since the fraction mentioned is basically the ratio of bears to all other animals, and 3 things greater than 1/3 couldn't add up to a whole, the proof is definitely unsound. Blast it.