If corn is 12% protein and weighs 56 pounds per bushel, and soybeans are 44% protein and weigh 60 pounds per bushel, what respective combinations of corn and soybean yields per acre produce about the same amount of protein.
To find out the respective combinations of corn and soybean yields per acre that produce about the same amount of protein, we need to consider the protein content of both crops and their respective weights.
Let's say we have x bushels of corn and y bushels of soybeans per acre.
The total protein from corn per acre is given by:
(Protein content of corn / 100) * (Weight of corn per bushel * Number of bushels of corn)
Similarly, the total protein from soybeans per acre is given by:
(Protein content of soybeans / 100) * (Weight of soybeans per bushel * Number of bushels of soybeans)
Since we want to find a combination that produces about the same amount of protein, we can set these equations equal to each other:
(Protein content of corn / 100) * (Weight of corn per bushel * Number of bushels of corn) = (Protein content of soybeans / 100) * (Weight of soybeans per bushel * Number of bushels of soybeans)
Now, let's substitute the given values:
(0.12) * (56 * x) = (0.44) * (60 * y)
Simplifying the equation further:
6.72x = 26.4y
To find the respective combinations, we need to find pairs of x and y that satisfy this equation. One way to do this is by selecting arbitrary values for x or y and solving for the other variable.
Let's assume x = 6 bushels of corn per acre:
6.72 * 6 = 26.4y
40.32 = 26.4y
y ≈ 1.53 bushels of soybeans per acre
So, with 6 bushels of corn per acre, you would need approximately 1.53 bushels of soybeans per acre to produce about the same amount of protein.
You can follow the same method to find other pairs of x and y that satisfy the equation and calculate different combinations of corn and soybeans per acre.
To determine the respective combinations of corn and soybean yields per acre that produce about the same amount of protein, we need to consider both the protein content and weight of the crops.
Let's represent the amount of corn yield per acre as C, and the amount of soybean yield per acre as S.
Given that corn is 12% protein, we can express the protein amount from the corn yield as 0.12C.
Similarly, since soybeans are 44% protein, we can represent the protein amount from the soybean yield as 0.44S.
To establish a balance between the protein amounts, we'll set up an equation: 0.12C = 0.44S.
Next, we'll consider the weight of the crops. We know that corn weighs 56 pounds per bushel, thus the weight of the corn yield is 56C.
Likewise, soybeans weigh 60 pounds per bushel, so the weight of the soybean yield is 60S.
To maintain an equitable weight, we will set up another equation: 56C = 60S.
Now, we have a system of equations:
0.12C = 0.44S (Equation 1)
56C = 60S (Equation 2)
To solve this system, we can use the method of substitution. Rearrange Equation 2 to solve for C:
C = (60S)/56
Substitute this value of C into Equation 1:
0.12((60S)/56) = 0.44S
Simplify:
0.12 * 60S = 0.44S * 56
7.2S = 24.64S
Eliminate the S terms:
7.2 = 24.64
This equation is not possible, and it implies that there is no combination of corn and soybean yields per acre that produces the same amount of protein.