In the lab, Lisa has two solutions that contain alcohol and is mixing them with each other. She uses 300 milliliters less of Solution A than Solution B. Solution A is 17% alcohol and Solution B is 11% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 201 milliliters of pure alcohol?

Let's solve the problem step by step.

Let:
- \( x \) be the amount of Solution B (in milliliters) that Lisa uses.
- \( x - 300 \) be the amount of Solution A (in milliliters) that she uses since she uses 300 milliliters less of Solution A than Solution B.

### Step 1: Express the amount of pure alcohol in each solution
- Solution A has 17% alcohol, so the amount of pure alcohol in Solution A is \( 0.17 \times (x - 300) \) milliliters.
- Solution B has 11% alcohol, so the amount of pure alcohol in Solution B is \( 0.11 \times x \) milliliters.

### Step 2: Set up the equation for the total amount of pure alcohol
The total amount of pure alcohol in the mixture is 201 milliliters. Therefore, the equation is:
\[
0.17(x - 300) + 0.11x = 201
\]

### Step 3: Solve the equation
First, distribute \( 0.17 \) in the first term:
\[
0.17x - 0.17 \times 300 + 0.11x = 201
\]
Simplify \( 0.17 \times 300 \):
\[
0.17x - 51 + 0.11x = 201
\]
Combine like terms (\( 0.17x + 0.11x \)):
\[
0.28x - 51 = 201
\]
Add 51 to both sides:
\[
0.28x = 252
\]
Now, divide both sides by 0.28:
\[
x = \frac{252}{0.28} = 900
\]

### Step 4: Conclusion
Lisa uses 900 milliliters of Solution B.

Would you like more details or have any questions about the solution?

Here are five related questions you might find interesting:
1. What is the amount of Solution A that Lisa uses?
2. How much total liquid (in milliliters) is in the resulting mixture?
3. What is the percentage of alcohol in the resulting mixture?
4. If Lisa used 100 milliliters more of Solution A, how would that change the final alcohol content?
5. How would the solution change if Solution B had a different alcohol concentration?

**Tip:** When working with percentage problems, always convert the percentage to a decimal before performing any calculations. This helps avoid errors and makes the math more straightforward.

Learn how to calculate the amount of Solution B used by Lisa in a mixture with Solution A, where Solution A contains 17% alcohol and Solution B contains 11% alcohol. The resulting mixture has 201 milliliters of pure alcohol. Detailed step-by-step solution provided. Suitable for Grades 7-9 students learning about percentages and linear equations.

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