A mixture contains 30% alcohol and 70% water. If 5 liters of pure alcohol are added to 20 liters of the mixture, what is the new percentage of alcohol in the mixture?
["How Adding Pure Alcohol Transforms a 30/70 Mixture: A Step-by-Step Calculation", "When working with alcoholic mixtures, accuracy in percentage calculations is crucial—especially when modifying concentrations by adding pure alcohol. In this article, we explore a practical example: what happens when we add 5 liters of pure alcohol to 20 liters of a 30% alcohol (and 70% water) mixture. This clear, data-driven breakdown will help you understand how concentration changes when pure alcohol is introduced.", "### Understanding the Original Mixture", "We begin with 20 liters of liquid that contains 30% alcohol.\n- Total volume of original mixture: 20 liters\n- Alcohol volume in the original mixture:\n ( 30% \ imes 20 = 0.30 \ imes 20 = 6 ) liters", "The remaining 70% is water:\n- Water volume: ( 70% \ imes 20 = 14 ) liters", "So, the original mixture consists of 6 liters of alcohol and 14 liters of water.", "### Adding Pure Alcohol", "We now add 5 liters of pure alcohol (100% alcohol) to this mixture:\n- New alcohol volume:\n ( 6, \ ext{L} + 5, \ ext{L} = 11, \ ext{L} )\n- Water volume remains unchanged: 14 liters\n- Total new volume of mixture:\n ( 20, \ ext{L} + 5, \ ext{L} = 25, \ ext{L} )", "### Calculating the New Alcohol Percentage", "To find the new percentage of alcohol:", "[\n\ ext{New % alcohol} = \left( \frac{\ ext{Total alcohol}}{\ ext{Total volume}} \right) \ imes 100 = \left( \frac{11}{25} \right) \ imes 100 = 44%\n]", "### Summary", "By adding 5 liters of pure alcohol to 20 liters of a 30% alcohol mixture (containing 6 liters of alcohol), the total alcohol increases to 11 liters in a 25-liter mixture. Therefore, the new alcohol percentage is 44%—a significant uplift from the original 30%.", "This calculation demonstrates how small additions of concentrated alcohol can substantially change a mixture’s strength—important knowledge for cocktails, fuel blends, and concentration-based industries.", "---", "Key Takeaways:\n- Always track volume and concentration separately.\n- Pure alcohol does not dilute, only increases the alcohol percentage.\n- Use simple algebra: (Original alcohol + Added alcohol) ÷ Total volume × 100 = New percentage.", "---", "If you want to adjust concentrations precisely, use the formula above—your mixtures will always reflect the true concentration!"]
