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The problem you're dealing with involves dilution of a peroxide solution. Here is a breakdown of the question:

### Problem Statement:
- You have a **120-milliliter** mixture of **30% peroxide** and water.
- A nurse dilutes the solution by pouring **30 milliliters** of this solution into a new container and then fills it with water until the total volume is **120 milliliters**.
- The final mixture contains **5% peroxide**.

### Question:
- At what point did the ratio of water to peroxide change? You need to explain how you know.

### Explanation:
The nurse is performing a **dilution** process. Here's the step-by-step analysis:

1. **Initial Solution**:
   - You have **120 mL** of a **30% peroxide solution**, meaning there are **0.3 × 120 = 36 mL of peroxide** in the solution and the rest is water.
   
2. **Pouring 30 mL**:
   - When the nurse pours **30 mL** of this solution, the amount of peroxide in that portion is **0.3 × 30 = 9 mL of peroxide** and **30 - 9 = 21 mL of water**.
   
3. **Dilution to 120 mL**:
   - The nurse then dilutes this 30 mL portion to a total of **120 mL** by adding **90 mL of water**. So the total water added is **21 mL (original water) + 90 mL (new water) = 111 mL of water** in the new container.
   - The amount of peroxide remains the same: **9 mL**.
   
4. **Final Concentration**:
   - The total volume of the new solution is **120 mL**, with **9 mL of peroxide**. This results in a peroxide concentration of:
     \[
     \frac{9}{120} \times 100 = 7.5\% \text{ peroxide}
     \]

This indicates there might be an error in the provided percentages in the problem (since diluting the solution to 120 mL with 9 mL of peroxide would give 7.5%, not 5%). Therefore, the question could involve a more careful check of units or assumptions.

Would you like a deeper dive into the calculations or perhaps clarification on another part of the problem?

Here are 5 related questions for deeper understanding:
1. How do you calculate the concentration of a solution after dilution?
2. Why does adding more solvent decrease the concentration of the solute?
3. How would the peroxide concentration change if the final volume was doubled?
4. How do different dilution factors impact the percentage concentration of solutions?
5. How can you use a proportion formula to predict final concentrations after dilution?

**Tip:** Always double-check units and proportions when working with dilution problems, as small errors can lead to significant differences in concentration estimates.

A 120-milliliter mixture of peroxide and water contained 30% peroxide. To dilute the mixture, a nurse poured 30 milliliters of this solution into a new container and filled it with water until the new mixture was 5% peroxide. At what point in this problem did the ratio of water to peroxide change? Explain how you know.

Learn how to solve a dilution problem involving a peroxide solution. A 120 mL mixture with 30% peroxide is diluted by pouring 30 mL into a new container and filling with water until the concentration becomes 5%. Step-by-step analysis suitable for students in Grades 10-12.

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