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Number 11, add in a chart. Include minimal key steps for the solving (make it short)

Here’s the solution for problem 11 using a chart:

### Chart Setup:
| Solution Type              | Volume (mL) | Concentration (%) | Amount of Acid (mL) |
|----------------------------|-------------|-------------------|---------------------|
| Initial Acid Solution      | 100         | 30                | \( 100 \times 0.30 = 30 \) |
| Added Acid Solution        | \( x \)     | 60                | \( x \times 0.60 \)       |
| Final Acid Solution        | \( 100 + x \) | 36              | \( (100 + x) \times 0.36 \) |

### Key Steps:
1. **Equation Setup:** Combine the amounts of acid in both solutions to equal the final acid amount:
   \[
   30 + 0.60x = 0.36(100 + x)
   \]

2. **Simplify and Solve:**
   \[
   30 + 0.60x = 36 + 0.36x
   \]
   \[
   0.60x - 0.36x = 36 - 30
   \]
   \[
   0.24x = 6
   \]
   \[
   x = \frac{6}{0.24} = 25
   \]

### Solution:
- **Volume of 60% acid solution to add:** 25 mL

Would you like more details or have any questions about this problem?

Here are some related questions to deepen your understanding:
1. What is the final concentration if you add 50 mL of a 60% solution instead?
2. How would the equation change if the final solution's concentration needed to be 40%?
3. What if the initial solution had a different volume, say 150 mL? How would that affect the solution?
4. How do you calculate the amount of acid in each solution?
5. What is the significance of maintaining the mass of the solute (acid) in dilution problems?

**Tip:** Always check if the calculated concentration matches the desired outcome to verify your solution.

What volume, in milliliters, of a 60% hydrochloric acid solution must be added to 100 mL of a 30% hydrochloric acid solution to make a 36% hydrochloric acid solution?

Solve how many milliliters of a 60% hydrochloric acid solution must be added to 100 mL of a 30% solution to achieve a 36% solution. This problem demonstrates mixture concepts and algebraic equations, suitable for students in Grades 9-11.

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