A man has some hens and cows. If the number of heads be 48 and number of feet be 140, how many cows are there ?

Options

A. 26
B. 25
C. 22
D. 23

Explanation

To solve the problem step by step, we will use the information given about the number of heads and feet of hens and cows.

### Step 1: Define Variables
Let:
- \( x \) = number of cows
- \( y \) = number of hens

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of heads (cows + hens) is 48:
\[ x + y = 48 \quad \text{(Equation 1)} \]

2. The total number of feet is 140. Cows have 4 feet each and hens have 2 feet each:
\[ 4x + 2y = 140 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 2:
\[ 2x + y = 70 \quad \text{(Equation 3)} \]

### Step 4: Solve the Equations
Now, we have two equations:
1. \( x + y = 48 \) (Equation 1)
2. \( 2x + y = 70 \) (Equation 3)

We can subtract Equation 1 from Equation 3 to eliminate \( y \):
\[ (2x + y) - (x + y) = 70 - 48 \]
This simplifies to:
\[ 2x - x + y - y = 22 \]
\[ x = 22 \]

### Step 5: Find the Number of Hens
Now that we have \( x = 22 \) (the number of cows), we can substitute this back into Equation 1 to find \( y \):
\[ 22 + y = 48 \]
\[ y = 48 - 22 \]
\[ y = 26 \]

### Conclusion
Thus, the number of cows is \( \boxed{22} \).