Question

You need to balance an 18% protein ration for weaned pigs weighing 40 lbs, using corn (9%) and soybean meal (45%). You need to mix 3 tons. What is the correct ratio of corn to soybean meal to achieve the 18% protein ration?

a) 1:1
b) 2:1
c) 1:2
d) 3:1

Answer 1

The correct ratio of corn to soybean meal to achieve an 18% protein ration using corn with 9% protein and soybean meal with 45% protein is 2:1, which corresponds to option (b) given in the question.

Step-by-step explanation:

To find the correct ratio of corn to soybean meal to achieve an 18% protein ration for weaned pigs weighing 40 lbs, we must create a dietary balance equation based on the given protein percentages for corn (9%) and soybean meal (45%). If we let x represent the amount of corn and y the amount of soybean meal, the total combination must yield 18% protein in the final 3-ton mixture.

We need to solve the equation 0.09x + 0.45y = 0.18(x + y). By rearranging the equation, we can find the ratio of x to y. Since we're not concerned about the exact amounts of corn and soybean meal but rather the ratio in which to mix them, this becomes a matter of simple algebra.

Solving for x/y yields the ratio of corn to soybean meal, which is 2:1. Therefore, for every part of soybean meal, two parts of corn should be used. This aligns with option (b) from the student's original question.

Remember, when working on such problems, to always ensure that the sum of your proportions equals to 1 (or 100%), representing the entire mixture.