Soybean meal is 16% protein and corn is 9% protein. How many pounds of each should be mixed to get a 350 lb mixture that is 12% protein?
s pounds of soy
c pounds of corn
s + c = 350
or c = 350 - s
.16 s + .09 c = .12 * 350 = 42
so
.16 s + .09(350 - s) = 42
etc
To solve this problem, we need to use a system of equations. Let's assume we need x pounds of soybean meal and y pounds of corn in the mixture.
We know that soybean meal is 16% protein and corn is 9% protein, and we want to end up with a 350 lb mixture that is 12% protein.
Step 1: Write equations based on the problem:
Equation 1: The total weight of the mixture is 350 lbs:
x + y = 350
Equation 2: The protein content of the mixture:
(0.16 * x) + (0.09 * y) = 0.12 * 350
Step 2: Solve the system of equations:
From equation 1: x = 350 - y
Substituting this into equation 2:
0.16(350 - y) + 0.09y = 0.12 * 350
Now, solve for y:
56 - 0.16y + 0.09y = 42
-0.07y = -14
y = 200
Plug in the value of y into equation 1:
x + 200 = 350
x = 150
Therefore, you would need 150 pounds of soybean meal and 200 pounds of corn to get a 350 lb mixture that is 12% protein.
To solve this problem, we can set up an equation based on the protein percentage in each ingredient.
Let's assume x represents the number of pounds of soybean meal, and y represents the number of pounds of corn.
According to the problem, we need to find a mixture that is 350 pounds and has a protein content of 12%.
First, let's set up the equation based on the protein content:
0.16x + 0.09y = 0.12 * 350
Simplifying this equation, we get:
0.16x + 0.09y = 42
Now, we need to add another equation to represent the total weight of the mixture:
x + y = 350
We now have a system of two equations:
0.16x + 0.09y = 42 ----(Equation 1)
x + y = 350 ----(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the elimination method:
Multiply Equation 2 by 0.16 to make the coefficients of x in both equations match:
0.16x + 0.16y = 56
Now, subtract Equation 1 from this new equation:
(0.16x + 0.16y) - (0.16x + 0.09y) = 56 - 42
0.16y - 0.09y = 14
0.07y = 14
y = 14 / 0.07
y = 200 pounds
Substitute the value of y back into Equation 2 to find the value of x:
x + 200 = 350
x = 350 - 200
x = 150 pounds
So, 150 pounds of soybean meal and 200 pounds of corn should be mixed to obtain a 350-pound mixture with a protein content of 12%.
Therefore, you should mix 150 pounds of soybean meal and 200 pounds of corn.