A man has some hens and some cows. If the total number of heads of hens and cows together is 50 and the number of feet of hens and cows together is 142, then the number of cows is

Options

A. 21
B. 25
C. 27
D. 29

Answer

To solve the problem, we need to set up equations based on the information given about the number of heads and feet of hens and cows.

### Step-by-Step Solution:

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

2. **Set Up the Equations**:
- From the problem, we know the total number of heads (which is the same as the total number of animals):
\[ x + y = 50 \quad \text{(Equation 1)} \]
- Each hen has 2 feet and each cow has 4 feet, so the total number of feet is:
\[ 2x + 4y = 142 \quad \text{(Equation 2)} \]

3. **Simplify Equation 2**:
- We can simplify Equation 2 by dividing everything by 2:
\[ x + 2y = 71 \quad \text{(Equation 3)} \]

4. **Substitute Equation 1 into Equation 3**:
- From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 50 - y \]
- Substitute this expression for \( x \) into Equation 3:
\[ (50 - y) + 2y = 71 \]

5. **Solve for \( y \)**:
- Combine like terms:
\[ 50 + y = 71 \]
- Subtract 50 from both sides:
\[ y = 71 - 50 \]
\[ y = 21 \]

6. **Conclusion**:
- The number of cows \( y \) is 21.

### Final Answer:
The number of cows is **21**.