Soymeal is 12% protein; cornmael is 6% protein. How many pounds of each should be mixed together in order to get 240lb mixture that us 9% protein
amount of 12% needed --- x lb
amount of 6% neede --- 240-x lb
solve for x
.12x + .06(240-x) = .09(240)
times 100
12x + 6(240-x) = 9(240)
I will let you finish it
To solve this problem, we can use a proportion method known as the "method of alligation." Here are the steps to find the solution:
Step 1: Assign variables
Let's assume the number of pounds of soymeal is x, and the number of pounds of cornmeal is y.
Step 2: Set up the equations
Based on the given information, we can set up two equations:
Equation 1: Protein in soymeal = 0.12x
Equation 2: Protein in cornmeal = 0.06y
Step 3: Set up the alligation diagram
We can use a diagram to represent the mixture proportions visually. Draw a line and mark it at the center.
On the left side, write 12 (the protein percentage of soymeal) and on the right side, write 6 (the protein percentage of cornmeal).
Now, you can divide the line into two sections. Let's label the section representing x as D and the section representing y as E.
D E
12 | 6
Step 4: Determine the ratio based on the desired protein percentage
Since we want a 9% protein mixture, we can place 9 in the center of the line, aligned with the D and E sections.
D E
12 | 6
9
To find the ratio of x to y, look at the difference between 12 and 9 (the distance from D to the center) and the difference between 9 and 6 (the distance from the center to E). The ratio of x to y is 3:3 or simply 1:1.
Step 5: Set up the equation based on the ratio
Taking the ratio into account, we can set up an equation:
x/y = 1/1
Step 6: Set up the equation based on the total weight of the mixture
Since the total weight of the mixture is 240 pounds, we can also set up an equation:
x + y = 240
Step 7: Solve the equations simultaneously
Using the equation from Step 5 (x/y = 1/1), we can rearrange it to x = y.
Substitute this value into the equation from Step 6:
x + x = 240
2x = 240
x = 240/2
x = 120
Step 8: Calculate the value of y
Since x = y, y = 120 as well.
Step 9: Check the answer
To verify that the solution is correct, let's find the protein percentage in the mixture:
Protein in soymeal = 0.12 * 120 = 14.4 lbs
Protein in cornmeal = 0.06 * 120 = 7.2 lbs
Total protein = 14.4 + 7.2 = 21.6 lbs
Protein percentage in mixture = (Total protein / Total weight of mixture) * 100
= (21.6 / 240) * 100
= 9%
Therefore, 120 pounds of soymeal and 120 pounds of cornmeal should be mixed together to obtain a 240-pound mixture with a 9% protein content.