Problem 1 The Dog Show There were 150

Problem 1 The Dog Show

There were 150 dogs at a dog show. Let A be the set of big dogs (over 50 pounds). Let B be the set of dogs with long hair. Let C be the set of dogs with spots. • 95 dogs had spots. • 8 dogs had spots and long hair and were big. • 12 dogs had only long hair. • 25 dogs had long hair and were big. • 23 dogs had only spots and were big. • 92 dogs were not big. • 49 had exactly two of these characteristics.

Long-haired Dogs Big Dogs Spotted Dogs

Long-haired Dogs Big Dogs 8 First, put the 8 big, long-haired, spotted dogs in the center! Spotted Dogs

Long-haired Dogs Big Dogs 12 8 23 Next, fill in the “only” information. Spotted Dogs

Long-haired Dogs Big Dogs 17 8 23 We know 25 dogs were big with long hair. There already 8 dogs in this space – so SUBTRACT. 25 -8=17 Spotted Dogs 12

Long-haired Dogs Big Dogs 17 8 23 AND 49 dogs share exactly 2 of these characteristics. So far we have 40 dogs here – we need 9 more! Spotted Dogs 12

Long-haired Dogs Big Dogs 12 17 8 23 9 95 dogs had spots. We have 40 so far -so we need 55 more. Spotted Dogs It says that 92 dogs were not big, if we add up what we have, find we are 16 short. So, there must be 16 dogs that are neither big nor spotted nor long haired.

Long-haired Dogs Big Dogs 12 17 8 9 23 There are 150 dogs total. Add the rest of the dogs and subtract from 150 to find the number of big dogs. 55 Spotted Dogs 16

Long-haired Dogs Big Dogs 12 17 10 8 9 23 55 Spotted Dogs 16