Soybean meal is 14% protein, cornmeal is 7% protein. how many pound of each should be mixed together in order to get 280-lb mixture that is 13% protein?
.14 s + .07 c = .13 (280)
and
s + c = 280
To solve this problem, we can use a method called the mixture problem or the weighted average method.
Let's first define the variables:
Let x be the amount of soybean meal (in pounds) to be mixed.
Then, the amount of cornmeal to be mixed would be (280 - x) pounds.
Now, we can set up the equation based on the protein content:
0.14x + 0.07(280 - x) = 0.13(280)
Let's break down the equation:
0.14x represents the protein content of the soybean meal (14% of x pounds),
0.07(280 - x) represents the protein content of the cornmeal (7% of (280 - x) pounds),
Finally, 0.13(280) represents the protein content of the mixture (13% of 280 pounds).
Now, let's solve the equation:
0.14x + 0.07(280 - x) = 0.13(280)
0.14x + 19.6 - 0.07x = 36.4
0.07x = 36.4 - 19.6
0.07x = 16.8
x = 16.8 / 0.07
x ≈ 240
According to the calculation, approximately 240 pounds of soybean meal should be mixed with 280 - 240 = 40 pounds of cornmeal to create a 280-pound mixture with a protein content of 13%.