Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed to get a 350-lb mixture that is 12% protein?
350 lb x 0.12 = 42 lb (total) of protein content.
let S be the mass of soybean meal and C be the mass of corn meal.
S + C = 350
0.16 S + 0.09 C = 42
Solve those two simultaneous equations
0.16 S + 0.16 C = 56
0.07 C = 14
C = 14/0.07 = ?
S = 350 - C = ?
To determine the quantities of soybean meal and corn meal needed to obtain a 350-lb mixture with 12% protein, we can set up the following equation:
Let x be the amount of soybean meal in pounds.
Then, 350 - x would be the amount of corn meal in pounds.
The equation to represent the protein content in the mixture is:
0.16x + 0.09(350 - x) = 0.12(350)
Now, let's solve the equation step by step:
0.16x + 0.09(350 - x) = 0.12(350)
0.16x + 31.5 - 0.09x = 42
0.16x - 0.09x = 42 - 31.5
0.07x = 10.5
x ≈ 150
So, approximately 150 pounds of soybean meal should be mixed with 200 pounds of corn meal to obtain a 350-lb mixture with 12% protein.