Final answer:
To make a 1-ton ration of a 24% protein ration using corn (21%) and soybean meal (31%), you will need to mix 0.7 tons of corn and 0.3 tons of soybean meal.
Step-by-step explanation:
To make a 1-ton ration of a 24% protein ration using corn (21%) and soybean meal (31%), let's assign variables to the amounts of corn and soybean meal. Let x represent the amount of corn (in tons) and y represent the amount of soybean meal (in tons). We have the following equation:
x + y = 1 (since we want a total of 1 ton of ration)
The protein content equation is:
0.21x + 0.31y = 0.24 (since we want a 24% protein ration)
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:
Multiplying the first equation by -0.21, we get:
-0.21x - 0.21y = -0.21
Adding this equation to the second equation, we eliminate x:
-0.21x - 0.21y + 0.21x + 0.31y = -0.21 + 0.24
0.1y = 0.03
y = 0.03 / 0.1 = 0.3 tons of soybean meal
Substituting this value back into the first equation, we can solve for x:
x + 0.3 = 1
x = 1 - 0.3 = 0.7 tons of corn
Therefore, you will need to mix 0.7 tons of corn and 0.3 tons of soybean meal to make a 1-ton ration of a 24% protein ration.