New concentration: \(\frac{150}{500 + x} = 20\%\)

["# Solving the Equation: New Concentration Formula (\frac{150}{500 + x} = 20%)", "Understanding equal fractions and concentration problems is essential in algebra, particularly when working with percentages and real-world applications such as chemical solutions, mixing problems, and statistics. One common equation students and professionals encounter involves solving for a variable in a concentration context—like finding the unknown quantity (x) in the equation:", "[\n\frac{150}{500 + x} = 20%\n]", "This article explores how to solve this concentration-style equation step-by-step, reinforces its significance, and explains its use in practical scenarios.", "---", "## What Is the Equation’s Meaning?", "The equation (\frac{150}{500 + x} = 20%) represents a proportion where 150 units of substance are dissolved in a total volume of (500 + x) units, resulting in a 20% concentration. Solving for (x) helps determine the additional volume needed to achieve the desired concentration—common in chemistry, pharmacology, and mixtures modeling.", "---", "## Step-by-Step Solution", "Step 1: Convert Percentage to Decimal", "Since percentages are proportional, convert 20% to decimal form:", "[\n20% = 0.20\n]", "Now rewrite the equation as:", "[\n\frac{150}{500 + x} = 0.20\n]", "Step 2: Eliminate the Denominator", "Multiply both sides by (500 + x) to isolate the fraction:", "[\n150 = 0.20(500 + x)\n]", "Step 3: Distribute the Decimal", "[\n150 = 0.20 \ imes 500 + 0.20x\n]\n[\n150 = 100 + 0.20x\n]", "Step 4: Solve for (x)", "Subtract 100 from both sides:", "[\n150 - 100 = 0.20x\n]\n[\n50 = 0.20x\n]", "Divide both sides by 0.20:", "[\nx = \frac{50}{0.20} = 250\n]", "---", "## Final Answer", "[\n\boxed{x = 250}\n]", "This means you need to add 250 units of solvent (or diluent) to the original 500 units to achieve a 20% concentration when 150 units of solute (dissolved substance) are present.", "---", "## Why This Matters: Real-World Applications", "This type of equation applies directly in:", "- Chemistry: Preparing stock solutions with accurate concentrations.\n- Pharmacy: Calculating medication dosages related to solution concentration.\n- Engineering & Manufacturing: Mixing materials to meet precise proportions.", "Understanding how to manipulate such equations equips you to solve complex mixture problems efficiently and ensures accuracy in scientific and industrial settings.", "---", "## Summary", "The equation (\frac{150}{500 + x} = 20%) demonstrates how fractions and percentages interrelate in concentration problems. By converting percentages to decimals and solving algebraically, we find that (x = 250). Mastering this step situates you to tackle similar real-world challenges where precise mixture calculations are required.", "---", "Keywords:\nconcentration equation solve (\frac{150}{500 + x} = 20%), algebra solving steps, real-world concentration problems, chemistry mixture calculation, solving for unknown in proportions, percentage concentration equation, algebra application."]