Soybean Meal Is 16% Protein; Cornmeal Is 8% Protein. How Many Pound Of Each Should Be Mixed Together In Order To Get 320 Lb. Mixture That Is 12% Protein?
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To solve this problem, you can use the concept of weighted averages and set up an equation.
Let's denote the pounds of soybean meal as "x" and the pounds of cornmeal as "y".
The equation for the total weight is:
x + y = 320 (equation 1)
The equation for the protein content is:
(0.16x + 0.08y) / 320 = 0.12 (equation 2)
Now, we have a system of two equations with two variables. We can solve it using the substitution method or the elimination method. Here, we'll use the substitution method.
First, we will rearrange equation 1:
x = 320 - y
Next, substitute this value of x into equation 2:
(0.16(320 - y) + 0.08y) / 320 = 0.12
Now, simplify the equation:
(51.2 - 0.16y + 0.08y) / 320 = 0.12
51.2 - 0.08y = 0.12 * 320
51.2 - 0.08y = 38.4
Rearrange the equation:
-0.08y = 38.4 - 51.2
-0.08y = -12.8
Now, solve for y:
y = (-12.8) / (-0.08)
y = 160
Substitute the value of y back into equation 1 to solve for x:
x + 160 = 320
x = 320 - 160
x = 160
Therefore, to get a 320 lb mixture that is 12% protein, you need 160 lbs of soybean meal and 160 lbs of cornmeal.