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:
- be the amount of Solution B (in milliliters) that Lisa uses.
- 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 milliliters.
- Solution B has 11% alcohol, so the amount of pure alcohol in Solution B is 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:
Step 3: Solve the equation
First, distribute in the first term: Simplify : Combine like terms (): Add 51 to both sides: Now, divide both sides by 0.28:
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:
- What is the amount of Solution A that Lisa uses?
- How much total liquid (in milliliters) is in the resulting mixture?
- What is the percentage of alcohol in the resulting mixture?
- If Lisa used 100 milliliters more of Solution A, how would that change the final alcohol content?
- 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.
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Math Problem Analysis
Mathematical Concepts
Percentages
Linear Equations
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9
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