A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140 then the number of hens will be:

Options

A. 22
B. 24
C. 26
D. 20

Answer

To solve the problem of finding the number of hens given the total number of heads and feet, we can set up a system of equations based on the information provided.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( x \) be the number of cows.
- Let \( y \) be the number of hens.

2. **Set Up the Equations:**
- From the problem, we know that the total number of heads (cows + hens) is 48. This gives us our first equation:
\[ x + y = 48 \quad \text{(Equation 1)} \]

- We also know that cows have 4 feet and hens have 2 feet. The total number of feet is 140. This gives us our second equation:
\[ 4x + 2y = 140 \quad \text{(Equation 2)} \]

3. **Simplify Equation 2:**
- We can simplify Equation 2 by dividing everything by 2:
\[ 2x + y = 70 \quad \text{(Equation 3)} \]

4. **Substitute Equation 1 into Equation 3:**
- From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 48 - y \]
- Substitute this expression for \( x \) into Equation 3:
\[ 2(48 - y) + y = 70 \]

5. **Solve for \( y \):**
- Expand and simplify:
\[ 96 - 2y + y = 70 \]
\[ 96 - y = 70 \]
- Rearranging gives:
\[ -y = 70 - 96 \]
\[ -y = -26 \]
\[ y = 26 \]

6. **Conclusion:**
- The number of hens \( y \) is 26.

### Final Answer:
The number of hens is **26**.