Question:** A tank contains 500 liters of a 30% salt solution. How much pure water must be added to reduce the concentration to 20%?
["Title: How Much Pure Water to Add to a 500L 30% Salt Solution to Get a 20% Salt Concentration?", "---", "Question:\nA tank contains 500 liters of a 30% salt solution. How much pure water must be added to reduce the concentration to 20%?", "---", "Answer:\nReducing the salt concentration in a solution by adding pure water is a common problem in chemistry, engineering, and water treatment. In this case, we begin with 500 liters of a 30% salt solution and want to dilute it to a 20% salt concentration. The key is understanding that adding pure water dilutes the solution without changing the total amount of salt—only spreading it over a larger volume.", "### Step-by-Step Explanation", "1. Calculate the amount of salt in the original solution:\nSalt = Volume × Concentration\nSalt = 500 liters × 30% = 500 × 0.30 = 150 liters of salt", "2. Let ( x ) be the amount of pure water (in liters) added.\nAfter adding, the total volume becomes ( 500 + x ) liters, and the salt concentration should be 20%.", "3. Set up the equation for the new concentration:\n[\n\frac{\ ext{Amount of salt}}{\ ext{Total volume}} = 20%\n]\n[\n\frac{150}{500 + x} = 0.20\n]", "4. Solve for ( x ):\nMultiply both sides by ( 500 + x ):\n[\n150 = 0.20(500 + x)\n]\nExpand the right side:\n[\n150 = 100 + 0.20x\n]\nSubtract 100 from both sides:\n[\n50 = 0.20x\n]\nDivide by 0.20:\n[\nx = \frac{50}{0.20} = 250\n]", "---", "### Final Answer:\nYou must add 250 liters of pure water to the tank to reduce the salt concentration from 30% to 20%.", "---", "### Why This Works\nPure water adds no salt but increases total volume, thereby lowering concentration. This principle is essential in chemistry for solution dilution and widely used in industries such as food processing, water treatment, and pharmaceuticals.", "---", "### FAQ\n- Q: Does adding water change the total salt amount?\nA: No, only the concentration decreases. The salt amount remains unchanged.", "- Q: Can you solve this using proportion instead of algebra?\nA: Yes! If 150 liters of salt make 30%, then 150 liters will make 20% in how many total liters?\n [\n \frac{150}{30} = \frac{500 + x}{20} \Rightarrow 5 = \frac{500 + x}{20} \Rightarrow 500 + x = 100 \ imes 20 = 1000 \Rightarrow x = 500\n ]\n That 500 liters includes the original 500 liters plus 250 liters of pure water—confirming our result.", "---", "Keywords:\nsalt solution dilution, salt concentration calculation, how to reduce salt concentration, 500 liter salt solution, pure water addition, salt concentration formula, chemical dilution problem, water treatment salt reduction, dilution of saline solution", "---", "Summary:\nTo reduce a 500-liter 30% salt solution to 20%, add 250 liters of pure water—a simple but critical principle used across scientific and industrial applications."]
