A farmer has enough food to feed 28 animals in his cattle for 9 days. How long would the food last, if there were 8 more animals in his cattle?

Answer

To solve the problem step by step, we will use the concept of inverse proportion since an increase in the number of animals will lead to a decrease in the number of days the food lasts.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The farmer has enough food to feed **28 animals** for **9 days**.

2. **Calculate the Total Animal Days**:
- Total animal days can be calculated as:
\[ \text{Total Animal Days} = \text{Number of Animals} \times \text{Number of Days} \]
- So, for 28 animals for 9 days:
\[ \text{Total Animal Days} = 28 \times 9 = 252 \text{ animal days} \]

3. **Determine the New Number of Animals**:
- If there are **8 more animals**, the total number of animals becomes:
\[ 28 + 8 = 36 \text{ animals} \]

4. **Calculate the Number of Days the Food Will Last for 36 Animals**:
- Let \( y \) be the number of days the food will last for 36 animals. Using the total animal days calculated earlier:
\[ \text{Total Animal Days} = \text{Number of Animals} \times \text{Number of Days} \]
- For 36 animals, we can set up the equation:
\[ 36 \times y = 252 \]

5. **Solve for \( y \)**:
- Rearranging the equation gives:
\[ y = \frac{252}{36} \]
- Performing the division:
\[ y = 7 \]

6. **Conclusion**:
- Therefore, the food will last for **7 days** if there are 36 animals.

### Summary of the Solution:
The food will last for **7 days** for 36 animals.