A zoo has few numbers of penguins and polar bears. The total number of heads of both of them is 60 and the total numbers of their feet is 160 . How many polar bears are there in the zoo ?

Options

A. 20
B. 40
C. 60
D. 80

Answer

To solve the problem of how many polar bears are in the zoo, we can use a system of equations based on the information provided.

### Step-by-Step Solution:

1. **Define Variables:**
Let \( p \) be the number of penguins and \( b \) be the number of polar bears.

2. **Set Up the Equations:**
We know two things from the problem:
- The total number of heads (which is equal to the total number of animals) is 60:
\[ p + b = 60 \quad \text{(1)} \]
- The total number of feet is 160. Penguins have 2 feet and polar bears have 4 feet:
\[ 2p + 4b = 160 \quad \text{(2)} \]

3. **Simplify Equation (2):**
We can simplify equation (2) by dividing everything by 2:
\[ p + 2b = 80 \quad \text{(3)} \]

4. **Subtract Equation (1) from Equation (3):**
Now, we can subtract equation (1) from equation (3):
\[ (p + 2b) - (p + b) = 80 - 60 \]
This simplifies to:
\[ b = 20 \]

5. **Find the Number of Penguins:**
Now that we know \( b \), we can substitute it back into equation (1) to find \( p \):
\[ p + 20 = 60 \]
Thus,
\[ p = 60 - 20 = 40 \]

6. **Conclusion:**
Therefore, the number of polar bears in the zoo is \( \boxed{20} \).