In a zoo, there are rabbits and pigeons. If their heads are counted these are 90 while their legs are 224. The number of pigeons in the zoo are 

Options

A. 70
B. 68
C. 72
D. 22

Answer

To solve the problem of finding the number of pigeons in the zoo, we can follow these steps:

### Step 1: Define the variables
Let the number of pigeons be \( X \). Since the total number of heads (pigeons + rabbits) is 90, the number of rabbits will be \( 90 - X \).

### Step 2: Set up the equation for legs
Pigeons have 2 legs each, and rabbits have 4 legs each. Therefore, the total number of legs can be expressed as:
\[ \text{Total legs} = 2X + 4(90 - X) \]

### Step 3: Substitute the total number of legs
According to the problem, the total number of legs is 224. So we can set up the equation:
\[ 2X + 4(90 - X) = 224 \]

### Step 4: Simplify the equation
First, distribute the 4:
\[ 2X + 360 - 4X = 224 \]
Now combine like terms:
\[ -2X + 360 = 224 \]

### Step 5: Isolate the variable
Subtract 360 from both sides:
\[ -2X = 224 - 360 \]
This simplifies to:
\[ -2X = -136 \]

### Step 6: Solve for \( X \)
Divide both sides by -2:
\[ X = \frac{-136}{-2} = 68 \]

### Conclusion
The number of pigeons in the zoo is \( 68 \).

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