soybean meal is 12% protein; cornmeal is 6% protein.How many pounds of each should be mixed together in order to get 240-lb mixture that is 10% protein%

How many pounds of the cornmeal should be in the mixture?_____pounds

How many pounds of the soybeans meals should be in the mixture?______pounds

Let the number of pounds of corn meal be x and the number of pounds of soybean meal be y.

x + y = 240, for obvious reasons.

(0.06 x + 0.12 y)/240 = 0.1 (the fracttion that is protein)

Solve those two equations for x and y, using algdebra.

The sccond equation can be rewritten as
0.06x + 0.12y = 24, or
x + 2y = 400

Take it from there

To solve this problem, we can use the method of mixture and proportions. Let's break down the steps:

Step 1: Assign variables
Let's assign variables to represent the pounds of soybean meal and cornmeal in the mixture. Let's say x represents the pounds of soybean meal and y represents the pounds of cornmeal.

Step 2: Set up equations
We need to set up two equations using the given information. The first equation represents the total weight of the mixture, which is 240 pounds:
x + y = 240

The second equation represents the protein content in the mixture. We are looking for a 10% protein content in the 240-pound mixture:
(0.12x + 0.06y) / 240 = 0.10

Step 3: Solve for x and y
Now, we can solve the equations simultaneously. Let's solve the first equation for x:
x + y = 240
x = 240 - y

Now substitute the value of x into the second equation:
(0.12(240 - y) + 0.06y) / 240 = 0.10

Step 4: Simplify and solve the equation
Let's simplify the equation and solve for y:
(28.8 - 0.12y + 0.06y) / 240 = 0.10
28.8 + 0.06y - 0.12y = 24
-0.06y = 24 - 28.8
-0.06y = -4.8
y = (-4.8) / (-0.06)
y = 80

Therefore, there should be 80 pounds of cornmeal in the mixture.

Step 5: Find x
Now substitute the value of y into the first equation to find x:
x + y = 240
x + 80 = 240
x = 240 - 80
x = 160

Therefore, there should be 160 pounds of soybean meal in the mixture.

To summarize:
The number of pounds of cornmeal in the mixture is 80 pounds.
The number of pounds of soybean meal in the mixture is 160 pounds.