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Set up Pearson's square to find the ratio of maize to sunflower.

Mathematics

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Answer

80 kg\text{80 kg}

Step-by-step solution

5 steps
  1. Set up Pearson's square to find the ratio of maize to sunflower.

    The desired DCP content for the ration is 20%.
    Maize contains 10% DCP.
    Sunflower contains 35% DCP.

    Maize (10% DCP)35−20=15 parts of Sunflower╲20% DCP╱Sunflower (35% DCP)20−10=10 parts of Maize\begin{array}{c c c} \text{Maize (10\% DCP)} & & 35 - 20 = 15 \text{ parts of Sunflower} \\ & \diagdown & \\ & 20\% \text{ DCP} & \\ & \diagup & \\ \text{Sunflower (35\% DCP)} & & 20 - 10 = 10 \text{ parts of Maize} \\ \end{array}
  2. Determine the ratio of maize to sunflower.

    The ratio of maize to sunflower is 10 parts maize to 15 parts sunflower.
    Ratio (Maize : Sunflower) = 10 : 15.
    This ratio can be simplified by dividing both numbers by 5:
    Ratio (Maize : Sunflower) = 2 : 3.

  3. Calculate the total parts in the ratio.

    Total parts = 2 (maize) + 3 (sunflower) = 5 parts.

  4. Calculate the proportion of maize in the mixture.

    Proportion of maize = Parts of MaizeTotal parts=25\frac{\text{Parts of Maize}}{\text{Total parts}} = \frac{2}{5}.

  5. Calculate the amount of maize needed for a 200 kg ration.

    Amount of maize = Proportion of maize ×\times Total ration weight
    Amount of maize = 25×200 kg\frac{2}{5} \times 200 \text{ kg}
    Amount of maize = 0.4×200 kg0.4 \times 200 \text{ kg}
    Amount of maize = 80 kg80 \text{ kg}

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