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To solve this problem, we need to calculate how much of the 95% alcohol mixture to add to the 210 mL of a 20% alcohol solution to create a 60% alcohol solution.

Let's denote:

- \( x \) = the volume of 95% alcohol solution to add (in mL).

### Step-by-Step Solution

1. **Set up the equation based on the amount of alcohol in each solution:**

   We have:
   - 210 mL of a 20% solution, which contains \( 0.20 \times 210 = 42 \) mL of pure alcohol.
   - \( x \) mL of a 95% solution, which contains \( 0.95x \) mL of pure alcohol.

   After adding these, the total volume of the solution will be \( 210 + x \) mL, and we want this mixture to be a 60% alcohol solution.

2. **Formulate the equation:**

   For the final mixture to be 60% alcohol, the amount of pure alcohol divided by the total volume should equal 60%:
   \[
   \frac{42 + 0.95x}{210 + x} = 0.60
   \]

3. **Solve for \( x \):**

   Multiply both sides by \( 210 + x \) to clear the denominator:
   \[
   42 + 0.95x = 0.60(210 + x)
   \]
   Expanding and simplifying:
   \[
   42 + 0.95x = 126 + 0.60x
   \]
   \[
   0.95x - 0.60x = 126 - 42
   \]
   \[
   0.35x = 84
   \]
   \[
   x = \frac{84}{0.35} = 240
   \]

### Answer

You will need to add **240 mL of the 95% solution** to obtain the desired 60% alcohol solution.

Would you like more details or have any questions?

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Here are five additional questions to consider:

1. What would happen if the target solution concentration were different, say 70%?
2. How much total solution will there be after adding the 95% solution?
3. Can we generalize this approach to create solutions of different concentrations?
4. What if you only had a 50% alcohol solution instead of 95%—could you still reach a 60% concentration?
5. How would this solution change if you started with a different initial volume?

**Tip:** In mixture problems, it's helpful to keep track of the total volume and concentration of each component to set up the correct equation.

You need a 60% alcohol solution. On hand, you have a 210 mL of a 20% alcohol mixture. You also have 95% alcohol mixture. How much of the 95% mixture will you need to add to obtain the desired solution?

Learn how to solve a mixture problem where you calculate how much of a 95% alcohol solution needs to be added to 210 mL of a 20% solution to create a 60% alcohol mixture. The problem involves using basic algebra and mixture formulas, suitable for high school students.

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