Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number od animal feet is 248, what is the total number of goats Deepak has ?

Options

A. 32
B. 36
C. 34
D. Cannot be determined

Answer

To solve the problem step by step, we can use the information given about the total number of heads and feet of the animals.

### Step 1: Define the variables
Let:
- \( x \) = number of goats
- \( y \) = number of hens

### Step 2: Set up the equations
From the problem, we know:
1. The total number of heads (goats + hens) is 90:
\[ x + y = 90 \quad \text{(Equation 1)} \]

2. The total number of feet (goats have 4 feet and hens have 2 feet) is 248:
\[ 4x + 2y = 248 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 1 for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 90 - x \]

### Step 4: Substitute \( y \) in Equation 2
Now, substitute \( y \) in Equation 2:
\[ 4x + 2(90 - x) = 248 \]

### Step 5: Simplify the equation
Distributing the 2:
\[ 4x + 180 - 2x = 248 \]
Combine like terms:
\[ 2x + 180 = 248 \]

### Step 6: Isolate \( x \)
Subtract 180 from both sides:
\[ 2x = 248 - 180 \]
\[ 2x = 68 \]

### Step 7: Solve for \( x \)
Divide both sides by 2:
\[ x = \frac{68}{2} = 34 \]

### Step 8: Conclusion
Thus, the total number of goats Deepak has is:
\[ \boxed{34} \]