A farmer kept a small number of sheep and ducks on her property. If there were 94 legs and 34 heads in total, how many sheep and ducks?

Let's solve this problem step by step using a system of equations.

### Step 1: Define the Variables
- Let \( x \) be the number of sheep.
- Let \( y \) be the number of ducks.

### Step 2: Set Up the Equations
1. **Heads equation**: Since each animal has one head, the total number of heads is given by:
   \[
   x + y = 34
   \]
2. **Legs equation**: Sheep have 4 legs and ducks have 2 legs, so the total number of legs is given by:
   \[
   4x + 2y = 94
   \]

### Step 3: Solve the System of Equations
1. **Simplify the legs equation** by dividing it by 2:
   \[
   2x + y = 47
   \]

2. **Subtract the heads equation from the simplified legs equation**:
   \[
   (2x + y) - (x + y) = 47 - 34
   \]
   Simplifying this, we get:
   \[
   x = 13
   \]

3. **Substitute \( x = 13 \) into the heads equation**:
   \[
   13 + y = 34
   \]
   Solving for \( y \), we get:
   \[
   y = 21
   \]

### Conclusion
The farmer has **13 sheep** and **21 ducks**.

Would you like more details on any step, or do you have any further questions?

Here are 5 related questions to explore further:
1. What if there were 120 legs and 40 heads? How many sheep and ducks?
2. How would the problem change if each animal had a different number of legs?
3. Can you find a general formula to solve similar problems?
4. What if the total number of heads was unknown, but the number of legs and animals was given?
5. How does this problem relate to systems of linear equations?

**Tip**: For word problems involving animals or people, consider each characteristic (like heads, legs, etc.) as an equation component to create a system of equations.

Learn how to solve a problem involving sheep and ducks with a detailed step-by-step solution. Understand how to set up and solve a system of equations to determine the number of sheep and ducks given the total number of legs and heads. Suitable for students in Grades 7-9.

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