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Let's walk through the problem:

We are given:
- Solution A: 40% alcohol, **1500 milliliters** used.
- Solution B: 12% alcohol, we need to find the **number of milliliters** used.
- The resulting mixture: 32% alcohol.

We will use **the concentration mixture formula** for this:

\[
\text{Alcohol from A} + \text{Alcohol from B} = \text{Alcohol in the final mixture}
\]

### Variables:
- Let \(x\) = milliliters of Solution B used.
- Alcohol in Solution A: \(1500 \times 0.40\)
- Alcohol in Solution B: \(x \times 0.12\)
- Total alcohol in the final mixture: \((1500 + x) \times 0.32\)

### Setting up the equation:
\[
1500 \times 0.40 + x \times 0.12 = (1500 + x) \times 0.32
\]

Now, solve for \(x\).

1. Calculate the terms:
   \[
   600 + 0.12x = 480 + 0.32x
   \]
2. Rearrange:
   \[
   600 - 480 = 0.32x - 0.12x
   \]
   \[
   120 = 0.20x
   \]
3. Solve for \(x\):
   \[
   x = \frac{120}{0.20} = 600 \, \text{milliliters}
   \]

### Answer:
Maya needs to use **600 milliliters of Solution B**.

---

Would you like me to explain any steps further or provide more examples? Here are some related questions for practice:

1. What if the target alcohol concentration was 35%? How would that change the answer?
2. How does the equation change if Solution B had a different concentration?
3. What if Solution A was only 1000 mL? How many milliliters of Solution B would be required then?
4. What happens if you mix two solutions with identical concentrations?
5. Can you use this method for non-alcoholic solutions, such as saltwater? How?

**Tip:** Always double-check the units when working with concentration problems to avoid simple mistakes.

In the lab, Maya has two solutions that contain alcohol and is mixing them with each other. Solution A is 40% alcohol and Solution B is 12% alcohol. She uses 1500 milliliters of Solution A. How many milliliters of Solution B does she use if the resulting mixture is a 32% alcohol solution?

Solve a mixture problem involving two alcohol solutions with different concentrations. Learn how to calculate the required volume of Solution B to reach a 32% alcohol concentration when mixed with 1500 mL of a 40% alcohol solution. Suitable for students in Grades 9-10.

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