Gopal has some hens and some goats. If the total number of animal heads are 43 and total number of feet are 142 ,how many hens does Gopal have?

Options

A. 28
B. 21
C. 15
D. can not be determined

Answer

To solve the problem of how many hens Gopal has, we can set up a system of equations based on the information given.

### Step-by-Step Solution:

1. **Define Variables:**
Let \( H \) be the number of hens and \( G \) be the number of goats.

2. **Set Up the Equations:**
- From the problem, we know that the total number of animal heads (hens + goats) is 43:
\[ H + G = 43 \quad \text{(Equation 1)} \]
- We also know that the total number of feet is 142. Hens have 2 feet and goats have 4 feet:
\[ 2H + 4G = 142 \quad \text{(Equation 2)} \]

3. **Simplify Equation 2:**
We can simplify Equation 2 by dividing the entire equation by 2:
\[ H + 2G = 71 \quad \text{(Equation 3)} \]

4. **Subtract Equation 1 from Equation 3:**
Now we will subtract Equation 1 from Equation 3:
\[ (H + 2G) - (H + G) = 71 - 43 \]
This simplifies to:
\[ G = 28 \]

5. **Find the Number of Hens:**
Now that we have the number of goats, we can substitute \( G \) back into Equation 1 to find \( H \):
\[ H + 28 = 43 \]
Solving for \( H \):
\[ H = 43 - 28 = 15 \]

6. **Conclusion:**
Therefore, the number of hens Gopal has is:
\[ \boxed{15} \]