A solution contains 40% alcohol. How much of a 70% alcohol solution must be added to 100 mL of the 40% solution to obtain a 50% alcohol solution?
["Title: How to Create a 50% Alcohol Solution by Mixing 40% and 70% Alcohol", "When working with alcohol solutions, achieving the right concentration is crucial—especially in laboratories, chemical processing, or pharmaceutical preparation. One common question is: How much of a 70% alcohol solution must be added to 100 mL of a 40% alcohol solution to obtain a 50% alcohol mixture?", "This article walks you through a step-by-step solution using algebra and the principle of alcohol content balance.", "---", "### Understanding the Problem", "We start with:\n- 100 mL of a 40% alcohol solution\n- An unknown volume of a 70% alcohol solution\n- The goal: Mix them to form a final solution of 50% alcohol concentration", "We are determining how much of the 70% solution (let’s call this x mL) must be added.", "---", "### Step 1: Calculate Alcohol Amounts", "The total amount of pure alcohol is what determines the concentration:", "- From the 40% solution:\n ( 100, \ ext{mL} \ imes 0.40 = 40, \ ext{mL of pure alcohol} )", "- From the 70% solution:\n ( x, \ ext{mL} \ imes 0.70 = 0.70x, \ ext{mL of pure alcohol} )", "---", "### Step 2: Total Volume and Final Concentration", "After mixing, the total volume becomes:\n( 100 + x, \ ext{mL} )", "We want the final solution to be 50% alcohol, so the total pure alcohol should be 50% of the total volume:\n( (100 + x) \ imes 0.50 )", "---", "### Step 3: Set Up the Equation", "Amount of alcohol from both solutions = Alcohol in final solution\n[\n40 + 0.70x = (100 + x) \ imes 0.50\n]", "---", "### Step 4: Solve the Equation", "Expand the right-hand side:\n[\n40 + 0.70x = 50 + 0.50x\n]", "Subtract ( 0.50x ) from both sides:\n[\n40 + 0.20x = 50\n]", "Subtract 40:\n[\n0.20x = 10\n]", "Divide by 0.20:\n[\nx = \frac{10}{0.20} = 50\n]", "---", "### Conclusion", "You must add 50 mL of the 70% alcohol solution to 100 mL of a 40% alcohol solution to obtain a 50% alcohol solution.", "---", "### Bonus Tips", "- Always calculate pure alcohol content (volume × percentage) when mixing solutions.\n- Use algebra for unknown mixing problems—this method ensures precision.\n- Such calculations are essential in chemistry, bartending, medicine, and industrial applications.", "---", "Keywords for SEO:\n50% alcohol solution, mixing alcohol solutions, how much 70% alcohol to add, 40% to 70% alcohol mixture, percent concentration calculation, alcohol dilution formula, lab mixing problem, alcohol concentration equation."]
