A one-ton batch of 12% grain mix is requested. You have available, cracked corn at 8% protein and soybean meal (SBM) at 40% protein. How many pounds of corn and SBM will make up the batch?

To find the correct mixture of cracked corn and soybean meal that results in a one-ton (or 2000 pounds) batch containing 12% protein, we can set up the problem using a system of equations based on the percentages of protein in each ingredient.

We know that:

• Cracked corn contributes 8% protein.

• Soybean meal contributes 40% protein.

• The final mix needs to contain 12% protein.

Let’s denote the amount of soybean meal as ( x ) pounds and the amount of cracked corn as ( 2000 - x ) pounds since the total weight must equal 2000 pounds.

To create the equation for the total protein content in the mixture, we calculate the protein from each component:

• Protein from soybean meal: ( 0.40x ) (since it's 40% protein)

• Protein from cracked corn: ( 0.08(2000 - x) )

The total protein from both components needs to equal 12% of 2000 pounds, which is 240 pounds of protein. Therefore, we can set up the equation:

[

0.40x + 0.08(2000 - x) = 240

]

Simpl