A poultry hatchery needs to hatch 300,000 chicks. How many eggs need to be set if the expected hatchability is 91%?

Question

BlackTom AI · Accepted Answer

Question restatement: A poultry hatchery needs to hatch 300,000 chicks. How many eggs need to be set if the expected hatchability is 91%?

Options to evaluate: 
1) 335,331
2) 333,519
3) 329,670
4) 392,670
5) 273,000

Step-by-step analysis:
Option 1 (335,331): This value would imply a higher number of eggs set than the baseline calculation suggests. If hatchability is 91%, the number of eggs required is calculated by dividing the desired hatchlings by the hatchability rate: Eggs_needed = 300,000 / 0.91 ≈ 329,670.33. Therefore, 335,331 eggs would overshoot the needed hatchlings, yielding more than 300,000 chicks, which is not consistent with the 91% assumption.

Option 2 (333,519): This is still larger than the precise calculation. Using the formula, 333,519 eggs would result in expected hatchlings of 333,519 × 0.91 ≈ 303,481, which is above the target of 300,000. Since the goal is to hit about 300,000 hatchlings, this option represents more eggs than necessary under 91% hatchability.

Option 3 (329,670): This value matches the standard division result: 300,000 ÷ 0.91 ≈ 329,670.33. Rounding to the nearest whole egg yields about 329,670 eggs. This aligns with the 91% hatchability assumption and the target hatch count, acknowledging that the expected hatchlings would be around 329,670 × 0.91 ≈ 299,999.7, effectively 300,000 when rounded.

Option 4 (392,670): This is substantially higher than the required amount. If you set 392,670 eggs at 91% hatchability, expected hatchlings would be 392,670 × 0.91 ≈ 357,070, far exceeding the 300,000 target. The math shows this option would overshoot significantly.

Option 5 (273,000): This option is lower than the needed number. At 91% hatchability, hatchlings would be 273,000 × 0.91 ≈ 248,430, which is well below the target. It underestimates the number of eggs needed to achieve 300,000 hatchlings.

Summary of reasoning: The core calculation uses Eggs_needed = Desired_hatchlings ÷ Hatchability. With 300,000 desired and 91% hatchability, that gives about 329,670 eggs. The third option is the one that aligns with this computation, while the other options either overshoot or undershoot based on the same 91% assumption.

A poultry hatchery needs to hatch 300,000 chicks. How many eggs need to be set if the expected hatchability is 91%?单项选择题

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