A solution is made by mixing 20% alcohol with 80% alcohol to get 5 liters of 50% alcohol. How much of each is used?
["Title: How to Mix 20% and 80% Alcohol to Make 5 Liters of 50% Alcohol – A Clear Solution Guide", "If you're wondering how to combine 20% alcohol with 80% alcohol to create exactly 5 liters of a 50% alcohol solution, this article breaks down the math and process clearly. Whether you're preparing laboratory solutions, cleaning agents, or adjusting alcohol concentrations for specific applications, understanding the correct proportions is essential.", "### The Problem Explained", "You want to make 5 liters of a 50% alcohol solution by mixing two alcohol concentrations:\n- One solution at 20% alcohol\n- Another at 80% alcohol", "The key is to determine how many liters of each to mix so the final result is 50% alcohol in 5 liters total.", "---", "### Step-by-Step Solution", "Let’s use algebra to solve this problem.", "Let:\n- ( x ) = liters of 20% alcohol\n- ( y ) = liters of 80% alcohol", "We know two things:\n1. The total volume must equal 5 liters:\n[ x + y = 5 ]", "2. The final alcohol concentration must be 50%:\nThe total amount of pure alcohol from both mixtures equals 50% of 5 liters (i.e., 2.5 liters):\n[ 0.20x + 0.80y = 0.50 \ imes 5 ]\n[ 0.20x + 0.80y = 2.5 ]", "---", "### Solving the Equations", "From the first equation:\n[ y = 5 - x ]", "Substitute into the second equation:\n[ 0.20x + 0.80(5 - x) = 2.5 ]\n[ 0.20x + 4 - 0.80x = 2.5 ]\n[ -0.60x + 4 = 2.5 ]\n[ -0.60x = 2.5 - 4 ]\n[ -0.60x = -1.5 ]\n[ x = \frac{1.5}{0.60} = 2.5 ]", "Now, substitute back to find ( y ):\n[ y = 5 - 2.5 = 2.5 ]", "---", "### Final Answer", "You need to mix:\n- 2.5 liters (50%) of 20% alcohol\n- 2.5 liters (80%) of 80% alcohol", "This combination yields 5 liters of a 50% alcohol solution, perfectly balanced for most applications.", "---", "### Why This Mix Works", "Mixing equal volumes of a low-concentration alcohol (20%) and a high-concentration alcohol (80%) strategically adjusts the overall strength. The midpoint (50%) lies exactly halfway when balanced linearly, proving how proportional mixing enables precision in chemistry and industry.", "---", "If you're approaching similar dilution problems—lasting stains, disinfectants, or quality control—remember:\nSatirical mixing is precise mixing. Know your percentages, use the equations, and balance your volumes well.", "---", "Keywords: alcohol mixing, 50% alcohol solution, 20% alcohol 80% alcohol mix, how to mix alcohol concentrations, alcohol dilution math, safe alcohol solution preparation"]
