Answer to November 29, 1999 Problem

The Winchester Zoo Problem

A visitor to the Winchester Zoo asked the zookeeper how many vultures and how many cows were in the zoo.

The zookeeper, a retired math teacher at the local high school, replied; "There are 45 heads and 150 feet."

How many vultures and cows are at the zoo?


Solution:

There are 30 cows and 15 vultures at the Winchester Zoo.

Let C = the number of cows
and V = the number of vultures.
From the total number of feet, we know that
V(2 feet/bird) + C(4 feet/cow) = 150 or
2V + 4C = 150

The total number of creatures in the zoo is
V + C = 45, so
V = 45 - C.

Now we can substitute this equation into the feet equation to obtain:
2(45 - C) + 4C = 150
90 - 2C + 4C = 150
2C = 60
C = 30 Cows and V = 45 - 30 = 15 Vultures

Correctly solved by:

1. Court Pifer Winchester, VA
2. Chris Moats Winchester, VA
3. Brandon Jaycox Winchester, VA
4. Jia Ran Rome, Italy
5. Michael Webber Winchester, VA
6. Jon Pence Winchester, VA
7. Chip Crawford Winchester, VA
8. Si Schiavone Winchester, VA
9. Laura Webb Winchester, VA
10. Tom Marino Winchester, VA