Hello, latinolp85!
Who assigned this problem?
A Venn diagram is the worst way to solve this problem!
In a group of cows and chickens i count 48 heads and 122 feet.
How many cows and fowl do i have? I spent several minutes trying to create a Venn diagram for this problem.
Let one circle be the set of cows.
Everything outside the circle is a fowl. Code:
* - - - - - - - - - - - - - - - *
| |
| |
| * - - - - - - * |
| | | |
| | | |
| | Cows | |
| | | |
| | | |
| * - - - - - - * |
| |
| |
| Fowl |
| |
| |
* - - - - - - - - - - - - - - - *
Let a second circle be the sets of Heads.
Everything outside the circle is a foot. Code:
* - - - - - - - - - - - - - - - *
| |
| |
| Feet |
| |
| |
| * - - - - - - * |
| | | |
| | | |
| | Heads | |
| | | |
| | | |
| * - - - - - - * |
| |
| |
* - - - - - - - - - - - - - - - *
Then our Venn diagram looks like this. Code:
* - - - - - - - - - - - - - - - *
| |
| |
| * - - - - - - * |
| | Cow | |
| | feet | |
| | * - - - + - - * |
| | | Cow | | |
| | | heads | | |
| * - - + - - - * | |
| | Fowl | |
| | heads | |
| * - - - - - - * |
| Fowl |
| feet |
* - - - - - - - - - - - - - - - *
Then I spent several more minutes trying to solve the problem
. . using this Venn diagram.
I failed abysmally. .I was forced to rely on Algebra.
. . This meant all the above work was a total waste of time.
Let = number of cows .and = number of fowl.
Since each cow has one head and four feet: .
Since each fowl has one head and two feet: .
We are told that: .
This becomes the system: .
. . which has the solution: .
Like I said, the worst way to solve it.