Soybean meal is 12% protein; Cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240lb mixture that is 8% protein?
s = pounds soy
c = pounds corn
s+c = 240 so c = (240-s)
.12 s + .06 c = .08 (240)
so
.12 s + .06(240-s) = .08 (240)
To solve this problem, we can use a basic algebraic approach called the "mixture problem". Let's break it down step by step:
Step 1: Define the variables.
Let's assume that the amount of soybean meal in pounds is represented by 'x', and the amount of cornmeal in pounds is represented by 'y'.
Step 2: Write down the equations based on the given information.
We are given that soybean meal is 12% protein, cornmeal is 6% protein, and the final mixture should be 8% protein. This information leads to two equations:
Equation 1: The total weight equation: x + y = 240
Equation 2: The protein equation: (0.12*x) + (0.06*y) = 0.08*240
Step 3: Solve the equations.
We can start by simplifying Equation 2:
0.12x + 0.06y = 19.2
Next, let's solve the system of equations formed by Equation 1 and the simplified version of Equation 2. There are different methods to solve this, but we will use substitution:
From Equation 1, we can express x in terms of y:
x = 240 - y
Substituting this value into the simplified Equation 2:
0.12(240 - y) + 0.06y = 19.2
28.8 - 0.12y + 0.06y = 19.2
28.8 - 0.06y = 19.2
-0.06y = 19.2 - 28.8
-0.06y = -9.6
y = (-9.6)/(-0.06)
y ≈ 160
Step 4: Calculate the value of x.
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
x = 240 - y
x = 240 - 160
x ≈ 80
Step 5: Check the solution.
Let's ensure that the solution satisfies the protein equation:
(0.12*80) + (0.06*160) = 0.08*240
9.6 + 9.6 = 19.2
19.2 = 19.2
Step 6: Interpret the results.
The solution indicates that 80 pounds of soybean meal and 160 pounds of cornmeal should be mixed together to create a 240-pound mixture that is 8% protein.
Therefore, to get the desired mixture, you would mix 80 pounds of soybean meal with 160 pounds of cornmeal.