soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280-lb mixture that is 125 protein?
To solve this question, we can set up a system of equations.
Let's assume that we need x pounds of soybean meal and y pounds of cornmeal to make the mixture.
According to the problem, the soybean meal is 14% protein, which means that 0.14x pounds of protein comes from the soybean meal.
Similarly, the cornmeal is 7% protein, which means that 0.07y pounds of protein comes from the cornmeal.
Now, considering that we want the final mixture to be 280 pounds with a protein content of 125, we can write the following equations:
Equation 1: x + y = 280 (the total weight of the mixture should be 280 pounds)
Equation 2: 0.14x + 0.07y = 125 (the total protein content in the mixture should be 125 pounds)
Now, we can solve this system of equations to find the values of x and y.
To solve Equation 1, we can rearrange it as follows:
x = 280 - y
Now, substitute this value of x into Equation 2:
0.14(280 - y) + 0.07y = 125
Simplify the equation:
39.2 - 0.14y + 0.07y = 125
39.2 - 0.07y = 125
-0.07y = 125 - 39.2
-0.07y = 85.8
Divide both sides by -0.07:
y = 85.8 / -0.07
y ≈ -1225.71
Since the weight of an ingredient cannot be negative, this solution is not valid. It means that there is no amount of cornmeal required to achieve a protein content of 125 in the mixture.
However, if we assume that the weight of the cornmeal is 0, the only ingredient left is the soybean meal. In that case, the weight of the soybean meal would be the total weight of the mixture, which is 280 pounds.
Therefore, you would need 280 pounds of soybean meal and 0 pounds of cornmeal to get a 280-pound mixture with a protein content of 125.