Final answer:
By creating equations from the given information about puppy paw colors and the total number of puppies, we calculate that there are 32 pure black puppies at the event.
Step-by-step explanation:
The question involves a mathematics problem that requires setting up equations based on the given information about puppies and their paw colors: pure white, pure black, and tri-colored. We know there are 100 puppies in total with 221 white paws and 34 brown paws. Tri-colored puppies have one white, one black, and two brown paws each. We can write the following system of equations where w, b, and t represent the number of white, black, and tri-colored puppies, respectively:
- w + b + t = 100 (total number of puppies)
- w*4 + t = 221 (total number of white paws considering pure white puppies have 4 white paws and tri-colored puppies have 1 white paw)
- t*2 = 34 (total number of brown paws, only present on tri-colored puppies, with two brown paws each)
From the third equation, we find that there are 17 tri-colored puppies (since 34 brown paws divided by 2 paws per tri-colored puppy equals 17). We can substitute t=17 in the second equation to find out the number of white puppies. Doing so, we get w*4 + 17 = 221, which simplifies to w*4 = 204, and therefore w = 51 (pure white puppies).
Now that we know the number of white and tri-colored puppies, we can use the first equation to find the number of pure black puppies. Substituting the known values, 51 + b + 17 = 100, simplifying we get b = 32.
Therefore, there are 32 black puppies at the event.