oxed{3}Question: A soil scientist mixes two fertilizers, one containing 15% nitrogen and another containing 40% nitrogen, to create 10 liters of a 25% nitrogen solution. How many liters of the 15% fertilizer are used?
["Title: How to Solve Fertilizer Blending Problems: A Step-by-Step Guide to Mixing 15% and 40% Nitrogen Fertilizers", "Meta Description:\nLearn how to solve the common fertilizer mixing problem: blending 15% and 40% nitrogen fertilizers to create a 25% nitrogen solution in 10 liters. This step-by-step guide uses algebra to determine the exact volume needed.", "---", "### Formula Question: A soil scientist mixes two fertilizers—one with 15% nitrogen and another with 40% nitrogen—to create 10 liters of a 25% nitrogen solution. How many liters of the 15% fertilizer are used?", "---", "### Step-by-Step Solution", "Creating a solution by mixing two fertilizers is a classic mixture problem solvable using algebra. Here’s how to apply it to this scenario:", "Let’s define:", "- ( x ) = volume (in liters) of the 15% nitrogen fertilizer\n- ( 10 - x ) = volume (in liters) of the 40% nitrogen fertilizer\n- Total volume = 10 liters\n- Desired concentration = 25% nitrogen", "### 1. Set up the equation using total nitrogen content", "The amount of nitrogen from each fertilizer must sum to the nitrogen in the final mixture:", "[\n0.15x + 0.40(10 - x) = 0.25 \ imes 10\n]", "### 2. Simplify the equation", "[\n0.15x + 4 - 0.40x = 2.5\n]", "Combine like terms:", "[\n-0.25x + 4 = 2.5\n]", "### 3. Solve for ( x )", "Subtract 4 from both sides:", "[\n-0.25x = 2.5 - 4\n]\n[\n-0.25x = -1.5\n]", "Divide both sides by -0.25:", "[\nx = \frac{-1.5}{-0.25} = 6\n]", "---", "### Final Answer", "The soil scientist uses 6 liters of the 15% nitrogen fertilizer.\nThe remaining 4 liters will be the 40% fertilizer to complete the 10-liter 25% nitrogen solution.", "---", "### Why This Method Works", "This algebraic approach ensures precision in fertilizer blending, critical for agricultural accuracy and crop health. By balancing percentages and volumes, you avoid over- or under-dosing nutrients—key for sustainable farming and soil management.", "---", "### Further Applications", "Similarly, this mixing logic applies to water treatment, pharmaceuticals, and chemical engineering. Mastering such equations improves problem-solving in science and industry.", "---", "Keywords: fertilizer mixing problem, 15% and 40% nitrogen solution, soil scientist, algebra method, mixture calculation, nitrogen percentage mix, chemical blending equations.", "---", "Optimized for SEO: This article targets farmers, agronomists, and science students searching for clear, practical chemistry and algebra applications in fertilizer blending. It emphasizes real-world relevance and step-by-step clarity, boosting visibility in search engines and reader engagement."]
