A group of farmers are plowing a field together. If we count both the cows and the farmers, there are a total of 36. If we count the legs, there are a total of 100. Find the number of farmers and the number of cows.

1. Problem Description

A group of farmers are plowing a field together. If we count both the cows and the farmers, there are a total of

3

6. If we count the legs, there are a total of

1

0

0. Find the number of farmers and the number of cows.

2. Solution Steps

Let $f$ be the number of farmers and $c$ be the number of cows.

We are given two pieces of information:

\begin{enumerate}

\item The total number of farmers and cows is

3

6. \item The total number of legs is

1

0

0. \end{enumerate}

We can write these as two equations:

$$f + c = 36$$

$$2f + 4c = 100$$

We can solve this system of equations. From the first equation, we have $f = 36 - c$. Substituting this into the second equation, we get:

$$2(36 - c) + 4c = 100$$

$$72 - 2c + 4c = 100$$

$$2c = 100 - 72$$

$$2c = 28$$

$$c = 14$$

Now we can find the number of farmers:

$$f = 36 - c = 36 - 14 = 22$$

Therefore, there are 22 farmers and 14 cows.

3. Final Answer

The number of farmers is 22, and the number of cows is 14.