In a zoo, there are rabbits and pigeons. If heads are counted there are 340 heads and if legs are counted there are 1060 legs. How many rabbits are there?

Options

A. 120
B. 190
C. 180
D. 170

Answer

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

### Step 1: Define Variables
Let:
- \( R \) = number of rabbits
- \( P \) = number of pigeons

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of heads (which is the sum of rabbits and pigeons) is 340:
\[ R + P = 340 \quad \text{(Equation 1)} \]
2. The total number of legs is 1060. Since each rabbit has 4 legs and each pigeon has 2 legs, we can express this as:
\[ 4R + 2P = 1060 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 2:
\[ 2R + P = 530 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( R + P = 340 \) (Equation 1)
2. \( 2R + P = 530 \) (Equation 3)

We can subtract Equation 1 from Equation 3:
\[ (2R + P) - (R + P) = 530 - 340 \]
This simplifies to:
\[ 2R - R + P - P = 190 \]
Thus, we have:
\[ R = 190 \]

### Step 5: Find the Number of Pigeons
Now that we have \( R \), we can substitute it back into Equation 1 to find \( P \):
\[ 190 + P = 340 \]
Subtracting 190 from both sides gives:
\[ P = 340 - 190 = 150 \]

### Conclusion
The number of rabbits in the zoo is \( R = 190 \).

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