There are some parrots and some tigers in a forest. If the total number of animal heads in the forest is 858 and the total number of animal legs is 1,846, what is of parrots in the forest?

Options

A. 845
B. 833
C. 800
D. 793

Answer

To solve the problem of finding the number of parrots in the forest, we can set up a system of equations based on the information given.

### Step-by-Step Solution:

1. **Define Variables:**
Let \( x \) be the number of parrots and \( y \) be the number of tigers.

2. **Set Up Equations:**
- Each animal has one head. Therefore, the total number of heads (parrots + tigers) is given by:
\[ x + y = 858 \quad \text{(Equation 1)} \]
- Parrots have 2 legs and tigers have 4 legs. Therefore, the total number of legs is given by:
\[ 2x + 4y = 1846 \quad \text{(Equation 2)} \]

3. **Simplify Equation 2:**
We can simplify Equation 2 by dividing everything by 2:
\[ x + 2y = 923 \quad \text{(Equation 3)} \]

4. **Subtract Equation 1 from Equation 3:**
Now we can subtract Equation 1 from Equation 3 to eliminate \( x \):
\[ (x + 2y) - (x + y) = 923 - 858 \]
This simplifies to:
\[ y = 65 \]

5. **Substitute \( y \) back into Equation 1:**
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ x + 65 = 858 \]
Solving for \( x \):
\[ x = 858 - 65 = 793 \]

6. **Conclusion:**
The number of parrots in the forest is \( \boxed{793} \).