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The problem on the screen asks you to solve a mixture problem involving alcohol solutions. Specifically, you are given:

- 480 mL of a 5% alcohol solution.
- A 90% alcohol mixture is also available.

You need to determine how much of the 90% alcohol mixture should be added to obtain a 10% alcohol solution.

### Let’s define the variables:
- Let \( x \) be the amount (in mL) of the 90% alcohol solution to add.

### Step-by-Step Solution:

1. **Alcohol in the 5% solution:**
   The amount of pure alcohol in the 480 mL of the 5% solution is:
   \[
   0.05 \times 480 = 24 \text{ mL of alcohol.}
   \]

2. **Alcohol in the 90% solution:**
   The amount of pure alcohol in \( x \) mL of the 90% solution is:
   \[
   0.90 \times x = 0.90x \text{ mL of alcohol.}
   \]

3. **Final amount of alcohol in the mixture:**
   After mixing, the total volume of the solution will be \( 480 + x \) mL. The desired concentration is 10%, so the total amount of alcohol should be:
   \[
   0.10 \times (480 + x) = 48 + 0.10x \text{ mL of alcohol.}
   \]

4. **Set up the equation:**
   The amount of alcohol from both the 5% solution and the 90% solution should add up to the total amount of alcohol in the final solution:
   \[
   24 + 0.90x = 48 + 0.10x
   \]

5. **Solve for \( x \):**
   Subtract \( 0.10x \) from both sides:
   \[
   24 + 0.80x = 48
   \]
   Subtract 24 from both sides:
   \[
   0.80x = 24
   \]
   Divide both sides by 0.80:
   \[
   x = \frac{24}{0.80} = 30 \text{ mL.}
   \]

### Final Answer:
You need to add **30 mL** of the 90% alcohol solution to obtain the desired mixture.

Would you like more details or have any questions about the steps? Here are 5 related questions to extend the learning:

1. What if the original solution had a different concentration, say 7%? How would the equation change?
2. How would the solution change if you needed to end with 15% alcohol instead of 10%?
3. Can this problem be solved using a system of linear equations? How?
4. How does the total volume affect the final alcohol concentration?
5. What if the available alcohol concentrations were 50% and 90% instead of 5% and 90%?

**Tip**: Always ensure that the units (mL, percentage) are consistent throughout the calculations to avoid errors.

You need a 10% alcohol solution. On hand, you have a 480 mL of a 5% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?

Learn how to solve a mixture problem involving 5% and 90% alcohol solutions. Determine how much of the 90% solution needs to be added to 480 mL of a 5% solution to create a 10% solution. A step-by-step solution is provided using systems of linear equations. Suitable for Grades 10-12.

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