5Question: A lab technician mixes two solutions containing 20% and 50% saline, respectively. If 3 liters of the first solution are combined with $ x $ liters of the second to create a 35% saline mixture, find $ x $.
["Title: How to Solve the Saline Mixing Problem: Finding the Correct Volume of 50% Saline Solution", "---", "Understanding how to mix saline solutions is essential in chemistry, healthcare, and industrial applications. In this article, we explore a classic mixture problem involving two saline solutions—20% and 50%—to demonstrate how to determine the volume of the stronger solution needed to produce a precise 35% saline mixture. We’ll walk through the math step-by-step, making it easy to replicate and apply to real-world scenarios.", "---", "### The Problem", "A lab technician combines 3 liters of a 20% saline solution with $ x $ liters of a 50% saline solution to produce a final mixture with a 35% saline concentration.", "Question: What is the value of $ x $?", "---", "### Step 1: Understand the components", "- First solution:\n Volume = 3 liters\n Concentration = 20% saline\n Salt amount = $ 3 \ imes 0.20 = 0.6 $ liters", "- Second solution:\n Volume = $ x $ liters\n Concentration = 50% saline\n Salt amount = $ x \ imes 0.50 = 0.5x $ liters", "- Final mixture:\n Total volume = $ 3 + x $ liters\n Desired concentration = 35%\n Salt amount = $ (3 + x) \ imes 0.35 $ liters", "---", "### Step 2: Set up the equation", "The total salt from both solutions equals the salt in the final mixture:", "$$\n\ ext{Salt from first} + \ ext{Salt from second} = \ ext{Salt in final mixture}\n$$", "$$\n0.6 + 0.5x = (3 + x) \ imes 0.35\n$$", "---", "### Step 3: Solve the equation", "Expand the right-hand side:", "$$\n0.6 + 0.5x = 1.05 + 0.35x\n$$", "Subtract $ 0.35x $ from both sides:", "$$\n0.6 + 0.15x = 1.05\n$$", "Subtract 0.6 from both sides:", "$$\n0.15x = 0.45\n$$", "Divide both sides by 0.15:", "$$\nx = \frac{0.45}{0.15} = 3\n$$", "---", "### Conclusion", "The technician must add 3 liters of the 50% saline solution to the 3 liters of 20% solution to create a 35% saline mixture. This problem highlights the power of algebra in solving practical laboratory and industrial mixing challenges.", "---", "### Key Takeaways for Lab Technicians and Students", "- Always convert percentages to decimal form for accurate calculations.\n- Use conservation of mass (salt) in mixture problems.\n- Set up equations based on volume and concentration relationships.\n- Solving step-by-step prevents common errors.", "---", "Whether you're in a lab, pharmacy, or manufacturing facility, mastering mixture problems ensures accurate, repeatable results. Practice with real-world concentrations to build confidence and precision.", "---", "Keywords: saline mixture, lab technician, concentration calculation, mixing solutions, 20% saline, 50% saline, algebra problem, chemistry practice, saline solution mixing", "Meta Description: Solve how much 50% saline solution must be mixed with 3 liters of 20% saline to make 35% solution — step-by-step calculation and explanation for lab professionals and students.", "---", "References:\n- Basic chemistry concentration principles\n- Algebraic equation modeling in science\n- Laboratory best practices for solution preparation", "---", "For more tips on solution mixing and lab techniques, subscribe to our science education newsletter!"]
