A soil scientist mixes three compost types to achieve a target C:N ratio of 25:1. Compost A has a C:N of 30:1, Compost B is 20:1, and Compost C is 15:1. She uses 40 kg of A, 35 kg of B, and 25 kg of C. What is the weighted average C:N ratio of the final mixture?
["How a Soil Scientist Achieves the Ideal 25:1 C:N Ratio by Mixing Three Compost Types", "In soil science, achieving the optimal carbon-to-nitrogen (C:N) ratio in compost is crucial for producing high-quality organic amendments that enhance soil fertility and microbial activity. A recent study highlights a precise method used by a soil scientist to balance C:N ratios by blending three distinct compost types — Compost A, B, and C — each with different nutrient profiles.", "### The Components: Understanding Individual C:N Ratios", "- Compost A: C:N ratio of 30:1\n- Compost B: C:N ratio of 20:1\n- Compost C: C:N ratio of 15:1", "These values reflect the balance of carbon (C) from organic matter and nitrogen (N) from plant and microbial waste, essential for effective decomposition and nutrient release in soil.", "### The Blend: Precise Ratios from Field Data", "The scientist carefully combined:\n- 40 kg of Compost A\n- 35 kg of Compost B\n- 25 kg of Compost C", "With total mass = 40 + 35 + 25 = 100 kg", "To find the weighted average C:N ratio of the mixture, we compute the contribution of carbon and nitrogen across all components and divide accordingly.", "---", "### Step 1: Calculate Total Carbon Content", "$$\n\ ext{Total C} = (40,\ ext{kg} \ imes 30) + (35,\ ext{kg} \ imes 20) + (25,\ ext{kg} \ imes 15)\n$$\n$$\n= 1200 + 700 + 375 = 2275,\ ext{kg C}\n$$", "### Step 2: Calculate Total Nitrogen Content", "$$\n\ ext{Total N} = (40,\ ext{kg} \ imes 1) + (35,\ ext{kg} \ imes 1) + (25,\ ext{kg} \ imes 1)\n$$\n$$\n= 40 + 35 + 25 = 100,\ ext{kg N}\n$$", "Note: Both carbon and nitrogen values are normalized per kg of compost material, so no scaling is needed.", "### Step 3: Compute Weighted Average C:N Ratio", "$$\n\ ext{C:N ratio} = \frac{\ ext{Total Carbon}}{\ ext{Total Nitrogen}} = \frac{2275}{100} = 22.75\n$$", "### Final Result:\nThe final compost mixture has a weighted average C:N ratio of 22.75:1, very close to the targeted 25:1 target — demonstrating how precise blending optimizes compost for soil health.", "---", "Why This Matters for Soil Scientists", "Approaching a balanced C:N ratio accelerates microbial breakdown, minimizes nitrogen immobilization, and ensures steady nutrient release. By mixing composts of different C:N values — as the soil scientist did — you tailor organic matter quality to specific soil needs, whether for agriculture, restoration, or urban greening.", "This method exemplifies the science behind composting: not just piling organic waste, but strategically managing its chemical profile through data-driven formulation.", "---", "### Summary", "| Compost Type | C:N Ratio | Quantity (kg) | Mass Contribution |\n|-------------|-----------|--------------|-------------------|\n| A | 30:1 | 40 | 1200 |\n| B | 20:1 | 35 | 700 |\n| C | 15:1 | 25 | 375 |\n| Total | – | – | 100 kg |\n| Total C | – | – | 2275 kg |\n| Total N | – | – | 100 kg |\n| Avg C:N | 22.75:1| – | 22.75:1 |", "By carefully measuring and blending three composts, the scientist achieved a near-ideal C:N ratio for optimal soil enhancement.", "---", "Keywords: Soil scientist, compost mixing, C:N ratio, organic matter, soil fertility, microbial activity, compost formulation, blended compost, carbon-to-nitrogen ratio, sustainable soil management."]
