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?
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To solve this problem, let's assume x pounds of soybean meal and y pounds of corn meal are needed to make a 350-lb mixture.
Let's start by setting up two equations based on the given information:
Equation 1: The total weight equation,
x + y = 350
Equation 2: The protein equation,
(0.16x + 0.09y)/(x + y) = 0.12
Now, let's solve this system of equations to find the values of x and y.
Step 1: Solve Equation 1 for x:
x = 350 - y
Step 2: Substitute x in Equation 2:
(0.16(350 - y) + 0.09y)/350 = 0.12
Step 3: Simplify and solve for y:
(56 - 0.16y + 0.09y)/350 = 0.12
(56 - 0.07y)/350 = 0.12
56 - 0.07y = 0.12 * 350
56 - 0.07y = 42
-0.07y = 42 - 56
-0.07y = -14
y = (-14)/(-0.07)
y = 200
Step 4: Substitute the value of y in Equation 1 to find x:
x + 200 = 350
x = 350 - 200
x = 150
Therefore, to get a 350-lb mixture that is 12% protein, you need 150 pounds of soybean meal and 200 pounds of corn meal.