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### Explanation of the Solutions:

1. **Problem 3a: Density of cattle in the United States**
   - Formula: \( \text{Density} = \frac{\text{Number of cattle}}{\text{Area}} \)
   - For the U.S., \( \text{Number of cattle} = 41.3 \text{ million} \) and \( \text{Area} = 3.797 \text{ million square miles} \).
   - The calculation is:  
     \[
     \frac{41.3}{3.797} = 10.87
     \]
   - This rounds to **10.9 cattle per square mile**.

2. **Problem 3b: Density of cattle in Republica**
   - Formula: \( \text{Density} = \frac{\text{Number of cattle}}{\text{Area}} \)
   - For Republica, \( \text{Number of cattle} = 12.1 \text{ million} \) and \( \text{Area} = 0.9084 \text{ million square miles} \).
   - The calculation is:  
     \[
     \frac{12.1}{0.9084} \approx 13.32
     \]
   - This rounds to **13.3 cattle per square mile**.

3. **Problem 3c: Absolute Comparison**
   - The sentence compares the absolute densities of cattle in both countries. It states that in Republica, there are **13.3 cattle per square mile**, while in the U.S., there are **10.9 cattle per square mile**.
   - The sentence provided correctly highlights that Republica has a **higher density of cattle** compared to the U.S.

4. **Problem 3d: Relative Comparison**
   - Formula:  
     \[
     \frac{13.3 - 10.9}{10.9} = 0.220 \times 100 = 22\%
     \]
   - Therefore, the sentence should say: "The density of cattle in Republica is **22% higher** than in the U.S."

### Clarifications
The calculations appear to be correct, and the written comparisons are appropriate based on the data. Good job!

### Would you like more details or have any questions?

### Here are five related questions to expand on the topic:
1. How would the density change if the cattle population in Republica increased by 10%?
2. What would happen to the U.S. cattle density if its area were reduced by 5%?
3. How can we compare egg consumption between Republica and the U.S. using a similar approach?
4. If Republica's area were doubled, what would be the new cattle density?
5. How could we compare population density between these two countries using this data?

### Tip:
When comparing percentages, always be sure to specify whether the difference is absolute or relative, as it can significantly affect the interpretation of data.

What is the density of cattle in the United States and Republica, and how do they compare both absolutely and relatively?

Understand how to calculate the density of cattle in the United States and Republica by dividing the number of cattle by the land area. Includes a detailed explanation of both absolute and relative percentage comparisons, showing how Republica has a 22% higher cattle density than the U.S.

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