Soybean meal is 18% protein, cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360lb. mixture that is 13% protein?

To solve this problem, we can use a technique called "mixture problems." Let's break down the steps to find the solution:

Step 1: Assign variables
Let's assign variables to the unknown quantities. We'll use:
- x: pounds of soybean meal
- y: pounds of cornmeal

Step 2: Set up equations
We need to set up an equation based on the given information. We can use the protein content to create the equations. The total protein content in the mixture is 13%, so:
- For soybean meal: x pounds * 18% protein = 0.18x
- For cornmeal: y pounds * 9% protein = 0.09y

Step 3: Create another equation based on the total weight of the mixture
The problem states that the total weight of the mixture is 360 pounds, so we can set up the equation:
- x pounds + y pounds = 360

Step 4: Set up the final equation
Since the final mixture should be 13% protein, the equation becomes:
- (0.18x + 0.09y) / 360 = 0.13

Step 5: Solve the equations
Now that we have two equations:
- x + y = 360
- (0.18x + 0.09y) / 360 = 0.13

We can solve this system of equations using a method like substitution or elimination.

Using the substitution method:
1. From the equation x + y = 360, solve for x:
x = 360 - y
2. Substitute this value of x into the second equation:
(0.18(360 - y) + 0.09y) / 360 = 0.13
3. Simplify and solve for y:
(64.8 - 0.18y + 0.09y) / 360 = 0.13
(64.8 - 0.09y) / 360 = 0.13
64.8 - 0.09y = 0.13 * 360
64.8 - 0.09y = 46.8
-0.09y = -18
y = (-18) / (-0.09)
y = 200

Step 6: Calculate x
Now that we know y = 200, we can substitute this value back into x + y = 360 to find x:
x + 200 = 360
x = 360 - 200
x = 160

So, to get a 360-pound mixture that is 13% protein, you need to mix 160 pounds of soybean meal with 200 pounds of cornmeal.