An agronomist prepares a custom nitrogen fertilizer blend by mixing three commercial grades: Grade A containing $46\%$ Nitrogen, Grade B containing $28\%$ Nitrogen, and Grade C containing $18\%$ Nitrogen in the ratio $2 : 3 : 5$ by weight. What is the overall percentage of Nitrogen in the final blended fertilizer? ________ % (round off to two decimal places).
Answer Key:
26.60
Step-by-Step Solution & Explanation
**Method 1: Weighted Average Composition**
Let the weights mixed be $2\text{ kg}, 3\text{ kg},$ and $5\text{ kg}$. Total blend weight $= 2 + 3 + 5 = 10\text{ kg}$.
- Nitrogen from Grade A $= 2 \times 0.46 = 0.92\text{ kg}$
- Nitrogen from Grade B $= 3 \times 0.28 = 0.84\text{ kg}$
- Nitrogen from Grade C $= 5 \times 0.18 = 0.90\text{ kg}$
$\text{Total Nitrogen} = 0.92 + 0.84 + 0.90 = 2.66\text{ kg}$
$\text{Blend Nitrogen } \% = \frac{2.66\text{ kg}}{10\text{ kg}} \times 100 = 26.60\%$