In the Pearson's Square example with 8.9% CP corn and 45.8% CP soybean meal to reach 15% CP, how many parts of the corn are required when the SBM part is 6.1?

In the Pearson's Square example with 8.9% CP corn and 45.8% CP soybean meal to reach 15% CP, how many parts of the corn are required when the SBM part is 6.1?

• A. 4.1
• B. 30.8
• C. 6.1
• D. 10.5

Answer: (B)

In this mixing problem, you use Pearson’s Square: the amounts of each ingredient are in the ratio of how far each ingredient’s CP is from the target CP. First, find how far each ingredient is from the target: - High-CP ingredient (soybean meal): 45.8% − 15% = 30.8 - Low-CP ingredient (corn): 15% − 8.9% = 6.1 The corn and soybean meal parts must be in the ratio 30.8 : 6.1. If the soybean meal part is 6.1, then the corn part is 30.8 to keep that ratio, so corn should be 30.8 parts. Quick check: with 6.1 parts SBM and 30.8 parts corn, the mixture’s CP is (6.1×45.8 + 30.8×8.9) ÷ (6.1+30.8) ≈ 15%.

In this mixing problem, you use Pearson’s Square: the amounts of each ingredient are in the ratio of how far each ingredient’s CP is from the target CP.

First, find how far each ingredient is from the target:

• High-CP ingredient (soybean meal): 45.8% − 15% = 30.8

• Low-CP ingredient (corn): 15% − 8.9% = 6.1

The corn and soybean meal parts must be in the ratio 30.8 : 6.1. If the soybean meal part is 6.1, then the corn part is 30.8 to keep that ratio, so corn should be 30.8 parts.

Quick check: with 6.1 parts SBM and 30.8 parts corn, the mixture’s CP is (6.1×45.8 + 30.8×8.9) ÷ (6.1+30.8) ≈ 15%.