There are some 'crow' and some elephants in a zoo. If the total number of animal heads in the zoo is 648 and total number of animals legs is 1426. What is that number of 'crow' in the zoo ?

Options

A. 56
B. 65
C. 835
D. 583

Answer

To solve the problem of finding the number of crows in the zoo, we can set up a system of equations based on the information provided.

### Step 1: Define Variables
Let:
- \( c \) = number of crows
- \( e \) = number of elephants

### Step 2: Set Up Equations
From the problem, we know:
1. Each animal has one head, so the total number of heads is given by:
\[ c + e = 648 \quad \text{(Equation 1)} \]
2. Crows have 2 legs and elephants have 4 legs, so the total number of legs is given by:
\[ 2c + 4e = 1426 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing everything by 2:
\[ c + 2e = 713 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( c + e = 648 \) (Equation 1)
2. \( c + 2e = 713 \) (Equation 3)

We can subtract Equation 1 from Equation 3:
\[ (c + 2e) - (c + e) = 713 - 648 \]
This simplifies to:
\[ e = 65 \]

### Step 5: Substitute Back to Find \( c \)
Now that we have \( e \), we can substitute it back into Equation 1 to find \( c \):
\[ c + 65 = 648 \]
Subtracting 65 from both sides gives:
\[ c = 648 - 65 = 583 \]

### Conclusion
The number of crows in the zoo is \( \boxed{583} \).

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