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This problem is about mixing two solutions of different alcohol concentrations to form a new solution with a desired concentration.

### Let’s break it down:

- You are asked to mix a **12% alcohol solution** and a **20% alcohol solution** to form a **15% alcohol solution**.
- The amount of the **20% alcohol solution** is given as **3 ounces**.
- Let the amount of the **12% alcohol solution** be **x ounces**.

The key idea is that the total amount of alcohol from both solutions must equal the amount of alcohol in the final mixture.

### Set up the equation:

1. The amount of alcohol in the **12% solution**:  
   \( 0.12x \) (since 12% means 0.12 times the amount of the solution).
   
2. The amount of alcohol in the **20% solution**:  
   \( 0.20 \times 3 = 0.60 \) ounces (since you have 3 ounces of a 20% solution).

3. The total amount of alcohol in the final **15% solution**:  
   The total solution is \( x + 3 \) ounces, and 15% of that is alcohol:  
   \( 0.15(x + 3) \).

### Now, set up the equation:

\[
0.12x + 0.60 = 0.15(x + 3)
\]

### Solve for \(x\):

1. Distribute on the right-hand side:
   \[
   0.12x + 0.60 = 0.15x + 0.45
   \]

2. Subtract \(0.12x\) from both sides:
   \[
   0.60 = 0.03x + 0.45
   \]

3. Subtract 0.45 from both sides:
   \[
   0.15 = 0.03x
   \]

4. Divide both sides by 0.03:
   \[
   x = 5
   \]

### Final Answer:
You need to mix **5 ounces** of the 12% alcohol solution.

Would you like further details or clarification? Here are five related questions for practice:

1. How do you solve a similar problem if the desired alcohol percentage is 18% instead of 15%?
2. What happens if you mix unequal amounts of two solutions with the same percentage?
3. How can this type of problem be modeled using a system of equations?
4. What would the equation look like if both solutions had the same concentration?
5. How do you adjust the equation if there is a different type of solution, like a sugar solution instead of alcohol?

**Tip:** Always keep track of your units (ounces in this case) and percentage (converted into decimals) in mixture problems to avoid errors.

How many ounces of a 12% alcohol solution must be mixed with 3 ounces of a 20% alcohol solution to make a 15% alcohol solution?

Learn how to solve a mixture problem involving the combination of a 12% and a 20% alcohol solution to create a final solution with a concentration of 15%. This step-by-step guide covers key algebraic concepts and is suitable for students in Grades 8-10.

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