You are composting -

5 lbs of leaves (C:N ~60:1)
5 lbs of grass clippings (C:N ~20:1)
3 lbs of food scraps (C:N ~15:1)
1 lb of newspaper (C:N ~150:1)

What is the C:N ratio of this compost mix?

Question

You are composting -

5 lbs of leaves (C:N ~60:1)
5 lbs of grass clippings (C:N ~20:1)
3 lbs of food scraps (C:N ~15:1)
1 lb of newspaper (C:N ~150:1)

What is the C:N ratio of this compost mix?

BlackTom AI · Accepted Answer

We need to determine the overall C:N ratio of the compost mix by combining the components according to their masses.
First, note each component’s C:N ratio (C:N): leaves = 60:1, grass clippings = 20:1, food scraps = 15:1, newspaper = 150:1.
A straightforward way to get the overall C:N is to compute a weighted average of these ratios, weighted by the mass of each component, since more mass of a given ratio contributes more to the total carbon and nitrogen balance.
Compute the weighted sum of C:N contributions:
- Leaves: 5 lb × 60 = 300
- Grass: 5 lb × 20 = 100
- Food scraps: 3 lb × 15 = 45
- Newspaper: 1 lb × 150 = 150
Total weighted C:N numerator = 300 + 100 + 45 + 150 = 595.
Total mass of the mix = 5 + 5 + 3 + 1 = 14 lb.
Now divide the total weighted carbon-to-nitrogen contributions by the total mass to obtain the overall C:N:
595 ÷ 14 ≈ 42.5.
Therefore, the C:N ratio of the mix is about 42.5:1.
Let's examine the other options:
- 50:1 would require a higher combined weight toward high-C:N components (e.g., more newspaper relative to others) than our mass distribution provides, so it’s too high given the actual masses.
- 35:1 is lower than 42.5 and would imply more low-C:N material (or less high-C:N material) influence than present; the weighted calculation shows this isn’t the case here.
- 28:1 is significantly lower, indicating a much larger share of low-C:N material, which contradicts the given masses (especially newspaper’s high C:N but small mass).
- 42.5:1 matches exactly the weighted-average calculation using the provided masses and per-item C:N ratios, so it is the correct result.
In short, applying a mass-weighted average of the component C:N ratios yields 42.5:1, which aligns with option '42.5:1.'

You are composting - 5 lbs of leaves (C:N ~60:1) 5 lbs of grass clippings (C:N ~20:1) 3 lbs of food scraps (C:N ~15:1) 1 lb of newspaper (C:N ~150:1) What is the C:N ratio of this compost mix? 单项选择题

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