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We can solve the problem by setting up equations based on the given information.

Let:
- \( x \) be the number of milliliters of Solution B that Ivan uses.
- \( x - 300 \) be the amount of Solution A he uses (since he uses 300 mL less of Solution A than Solution B).

We know that:
- Solution A is 11% alcohol.
- Solution B is 18% alcohol.
- The total amount of pure alcohol in the mixture is 286 milliliters.

The amount of alcohol in Solution A is:
\[
0.11 \times (x - 300)
\]

The amount of alcohol in Solution B is:
\[
0.18 \times x
\]

The total amount of pure alcohol from both solutions is the sum of the above two expressions, and this must equal 286 milliliters. So we set up the equation:
\[
0.11(x - 300) + 0.18x = 286
\]

Now let's solve this equation.The solution to the equation is \( x = 1100 \). 

This means Ivan uses **1100 milliliters** of Solution B.

Would you like a more detailed explanation of the steps? Here are some related questions:

1. How is the concentration of alcohol in a solution calculated?
2. What if the percentage of alcohol in Solution B was different—how would that affect the result?
3. Can you explain the importance of setting up equations in solving mixture problems?
4. How would the solution change if Ivan used the same amount of Solution A and Solution B?
5. How could we model this problem using a system of linear equations?

**Tip**: Always double-check your setup when working with percentage-based problems to avoid small calculation errors.

In the lab, Ivan has two solutions that contain alcohol and is mixing them with each other. He uses 300 milliliters less of Solution A than Solution B. Solution A is 11% alcohol and Solution B is 18% alcohol. How many milliliters of Solution B does he use if the resulting mixture has 286 milliliters of pure alcohol?

Learn how to solve a mixture problem involving two alcohol solutions, where Solution A is 11% alcohol and Solution B is 18% alcohol. The goal is to find the amount of Solution B needed if the resulting mixture contains 286 mL of pure alcohol. Suitable for high school students.

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