A solution contains 40% alcohol. How many liters of pure alcohol must be added to 10 liters of this solution to make a 60% alcohol solution?
["Title: How to Convert a 40% Alcohol Solution to a 60% Alcohol Solution: A Step-by-Step Calculation", "---", "Introduction\nCountless households and industrial applications rely on alcohol solutions, but understanding how to adjust their strength is essential for safety, cost, and effectiveness. If you have 10 liters of a solution containing 40% alcohol and want to increase its strength to 60% by adding pure alcohol, here’s exactly how to calculate the amount of alcohol to add.", "---", "### Understanding the Problem", "You begin with 10 liters of a 40% alcohol solution, meaning:", "- Volume of pure alcohol = 40% of 10 liters = 4 liters", "You want to increase the concentration to 60% by adding only pure alcohol (100% alcohol) to this 10-liter base.", "---", "### Key Concept: Add Pure Alcohol to Current Solution", "Let ( x ) be the amount (in liters) of pure alcohol to add.", "After adding ( x ) liters:", "- Total volume = ( 10 + x ) liters\n- Total pure alcohol = initially 4 liters + ( x ) liters = ( 4 + x ) liters", "We want the final concentration to be 60%, so:", "[\n\frac{4 + x}{10 + x} = 0.60\n]", "---", "### Step-by-Step Equation Solving", "Multiply both sides by ( 10 + x ):", "[\n4 + x = 0.60(10 + x)\n]", "Expand right side:", "[\n4 + x = 6 + 0.60x\n]", "Subtract ( 0.60x ) from both sides:", "[\n4 + 0.40x = 6\n]", "Subtract 4:", "[\n0.40x = 2\n]", "Divide by 0.40:", "[\nx = \frac{2}{0.40} = 5\n]", "---", "### Conclusion", "To convert 10 liters of a 40% alcohol solution into a 60% alcohol solution, you must add:", "5 liters of pure alcohol.", "---", "This precise calculation ensures accurate concentration without guesswork—critical in both home use and commercial blending.", "---", "Keywords: 40% alcohol solution, how to add pure alcohol, alcohol concentration calculation, 60% alcohol solution, margin calculation, pure alcohol addition, chemistry problem solving", "Meta Description: Want to increase 10 liters of 40% alcohol to 60%? Learn exactly how many liters of pure alcohol to add—step-by-step with math.", "---", "Bonus Tip: Always verify concentration calculations before blending, especially in safety-sensitive or industrial settings."]
