soybean meal is 14% protein, corn meal is 7% protein how many lbs of each should be mixed together in order to get 280 lb mixture that is 13% protein>>?
how many lbs of cornmeal should be in the mixture?
how many lbs of soybean should be in the mixture?
i think 21
To find the quantities of soybean meal and corn meal needed to create a 280 lb mixture with a 13% protein content, you can follow these steps:
Step 1: Assign variables
Let x be the amount (in pounds) of soybean meal.
Let y be the amount (in pounds) of corn meal.
Step 2: Set up equations based on protein content
The protein content in soybean meal is 14%, which means 0.14 of the mixture is protein.
The protein content in corn meal is 7%, which means 0.07 of the mixture is protein.
To calculate the protein content in the mixture, you multiply the protein percentage by the weight of the component:
0.14x is the protein content contributed by the soybean meal.
0.07y is the protein content contributed by the corn meal.
The total protein content in the mixture should be 13% of 280 lb, which means 0.13 of the mixture is protein:
0.14x + 0.07y = 0.13 * 280
Step 3: Set up the weight equation
Since we want a 280 lb mixture:
x + y = 280
Step 4: Solve the system of equations
You can solve the system of equations with two variables. One way to do this is by substitution or elimination. I'll use the elimination method here.
Multiply the weight equation by -0.14 to eliminate x:
-0.14x - 0.14y = -0.14 * 280
Then add the equations together:
0.14x + 0.07y = 0.13 * 280
-0.14x - 0.14y = -0.14 * 280
---------------------------
-0.07y = -0.01 * 280
Step 5: Calculate the solution
Simplifying the equation:
-0.07y = -2.8
Divide both sides of the equation by -0.07:
y = -2.8 / (-0.07)
y = 40
Now, substitute the value of y back into the weight equation to solve for x:
x + 40 = 280
x = 280 - 40
x = 240
Therefore, you need 240 lb of soybean meal and 40 lb of corn meal to create a 280 lb mixture with a 13% protein content.