Math Problem Statement

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?

Solution

Let's solve the problem step by step.

Let:

  • xx be the amount of Solution B (in milliliters) that Lisa uses.
  • x300x - 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×(x300)0.17 \times (x - 300) milliliters.
  • Solution B has 11% alcohol, so the amount of pure alcohol in Solution B is 0.11×x0.11 \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(x300)+0.11x=2010.17(x - 300) + 0.11x = 201

Step 3: Solve the equation

First, distribute 0.170.17 in the first term: 0.17x0.17×300+0.11x=2010.17x - 0.17 \times 300 + 0.11x = 201 Simplify 0.17×3000.17 \times 300: 0.17x51+0.11x=2010.17x - 51 + 0.11x = 201 Combine like terms (0.17x+0.11x0.17x + 0.11x): 0.28x51=2010.28x - 51 = 201 Add 51 to both sides: 0.28x=2520.28x = 252 Now, divide both sides by 0.28: x=2520.28=900x = \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.