Solution: Let the amount of saline in the first solution be $ 0.20 \times 3 = 0.6 $ liters. The second solution contributes $ 0.50x $ liters of saline. The total volume is $ 3 + x $ liters, and the total saline is $ 0.35(3 + x) $. Setting up the equation:

["SEO-Optimized Article: Solving Saline Concentration Equations for Precise Medical Solutions", "Understanding saline concentration is critical in medical preparation, dental treatments, and laboratory applications. One common challenge involves mixing two saline solutions to achieve a target volume and concentration. This SEO-optimized guide walks you through a step-by-step solution using a rational equation model. Whether you're a healthcare professional or a science student, mastering this problem helps ensure accurate, safe saline preparation.", "---", "### Step-by-Step Solution: Balancing Saline in Two Solutions", "When preparing saline solutions, exact concentrations and volumes matter to avoid under- or overdosing. Consider a scenario where a first saline solution contributes a fixed volume, and a second solution adds saline proportionally to its volume.", "Let’s define the variables:\n- First solution saline contribution: $ 0.20 \ imes 3 = 0.6 $ liters\n- Second solution saline contribution: $ 0.50x $ liters (where $ x $ liters is added)\n- Total volume: $ 3 + x $ liters\n- Total saline: $ 0.35(3 + x) $ liters", "Now, we set up the equation that expresses total saline from both sources equal to the target saline:", "[\n\ ext{Saline from first solution} + \ ext{Saline from second solution} = \ ext{Total saline}\n]", "Substituting values:", "[\n0.6 + 0.50x = 0.35(3 + x)\n]", "---", "### Solving the Equation", "Now solve for $ x $, the variable representing volume of the second solution:", "1. Expand the right-hand side:\n[\n0.6 + 0.50x = 1.05 + 0.35x\n]", "2. Subtract $ 0.35x $ from both sides:\n[\n0.6 + 0.15x = 1.05\n]", "3. Subtract $ 0.6 $ from both sides:\n[\n0.15x = 0.45\n]", "4. Divide both sides by $ 0.15 $:\n[\nx = \frac{0.45}{0.15} = 3\n]", "---", "### Final Answer", "The required volume $ x $ of the second saline solution is 3 liters. This means:", "- Total volume = $ 3 + 3 = 6 $ liters\n- Total saline = $ 0.35 \ imes 6 = 2.1 $ liters\n- Confirm: $ 0.6 + 0.50 \ imes 3 = 0.6 + 1.5 = 2.1 $ liters — verification passes!", "---", "### Why This Equation Matters", "Using this structured equation-based approach ensures precision in hospital settings and research labs. It helps standardize saline mixing protocols, minimize errors, and improve patient safety. For professionals seeking reliable sanitization or infusion solutions, mastering saline concentration math is indispensable.", "---", "Keywords: saline concentration equation, medical solution mixing, saline volume calculation, importance of saline in medicine, step-by-step saline solution solving, healthcare math, precise saline preparation, solving saline equation, volume and concentration balance", "Use this clear, equation-driven method to confidently handle saline mixing tasks and enhance clinical accuracy."]