\section*{Task 1 - V11011}

At VEG Neuendorf, 82.5 ha are planted with cereals, 48.72 ha with root crops, and 20.47 ha with lucerne. The root crop areas are to receive 34 kg of phosphoric pentoxide (P2O5) per hectare, the lucerne areas 20 kg, and the cereal areas 17.5 kg.

How many decitons of superphosphate are required if it contains 17.3 percent phosphoric pentoxide?
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For the Hackfrucht areas, \(48.72 \cdot 34 \mathrm{~kg}=1656.48 \mathrm{~kg} P_{2} O_{5}\) are required. For the Lucerne areas, \(20.47 \cdot 20 \mathrm{~kg}=409.40 \mathrm{~kg} P_{2} O_{5}\) are required. For the grain areas, \(82.5 \cdot 17.5 \mathrm{~kg}=1443.75 \mathrm{~kg} P_{2} O_{5}\) are required. In total, \(3509.83 \mathrm{~kg} \mathrm{P}_{2} \mathrm{O}_{5}\) are required.

Superphosphate contains 17.3 percent \(P_{2} O_{5}\), so in total \(\frac{3509.63}{0.173} \mathrm{~kg} \approx 20286 \mathrm{~kg}\) of Superphosphate are required. Since one decitonne equals 100 kg, 202.86 decitonnes of Superphosphate are required.