1. **State the problem:** We have 32 grams of a 25% antiseptic solution and want to dilute it to a 10% solution by adding distilled water.
2. **Formula used:** The amount of antiseptic remains the same before and after dilution. Use the formula:
$$C_1V_1 = C_2V_2$$
where $C_1$ and $V_1$ are the initial concentration and volume, and $C_2$ and $V_2$ are the final concentration and volume.
3. **Identify known values:**
- $C_1 = 25\% = 0.25$
- $V_1 = 32$ grams
- $C_2 = 10\% = 0.10$
- $V_2 = V_1 + x$ where $x$ is the amount of distilled water added.
4. **Set up the equation:**
$$0.25 \times 32 = 0.10 \times (32 + x)$$
5. **Calculate:**
$$8 = 0.10 \times (32 + x)$$
6. **Divide both sides by 0.10:**
$$\frac{8}{\cancel{0.10}} = \cancel{0.10} \times \frac{32 + x}{\cancel{0.10}}$$
$$80 = 32 + x$$
7. **Solve for $x$:**
$$x = 80 - 32 = 48$$
**Answer:** You should add 48 grams of distilled water to reduce the solution to 10%.
Solution Dilution A5Eb64
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