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 15% Protein?

To solve this problem, we can use a system of equations. Let's denote the number of pounds of soybean meal as 'x' and the number of pounds of cornmeal as 'y'.

First, let's establish the two equations given the information given in the problem:

Equation 1: The total weight of the mixture is 320 pounds: x + y = 320

Equation 2: The protein content in the mixture can be calculated by multiplying the protein content of each ingredient by its respective weight and then dividing by the total weight of the mixture. The equation for protein content becomes: (0.16x + 0.08y) / 320 = 0.15

Now we have a system of two equations that we can solve to find the values of x and y.

1. Solve Equation 1 for x:
x = 320 - y

2. Substitute x into Equation 2:
(0.16(320 - y) + 0.08y) / 320 = 0.15

3. Simplify Equation 2:
(51.2 - 0.16y + 0.08y) / 320 = 0.15

4. Combine like terms:
(51.2 - 0.08y) / 320 = 0.15

5. Multiply both sides of the equation by 320 to eliminate the denominator:
51.2 - 0.08y = 0.15*320

6. Simplify and solve for y:
51.2 - 0.08y = 48

7. Subtract 51.2 from both sides:
-0.08y = -3.2

8. Divide both sides by -0.08:
y = 40

Now that we have found the value for y, we can substitute it back into Equation 1 to find the value for x:

x + 40 = 320
x = 320 - 40
x = 280

So, you would need 280 pounds of soybean meal and 40 pounds of cornmeal to obtain a 320-pound mixture that is 15% protein.