Soybean meal is 18% protein, cornmeal is 9% protein. How many pounds of each should be mixed together in order to get a 360-lb mixture that is 10% protein?
Cornmeal-how many pounds:__________
Soybean meal-how many pounds:______
To solve this problem, we can use a system of equations.
Let's assume that x pounds of cornmeal is mixed with (360 - x) pounds of soybean meal.
We can set up two equations based on the given information:
Equation 1: Protein in cornmeal + Protein in soybean meal = Total protein in mixture
0.09x + 0.18(360 - x) = 0.10(360)
Equation 2: We need a total of 360 pounds of mixture
x + (360 - x) = 360
Now, let's solve the equations:
Equation 1:
0.09x + 0.18(360 - x) = 0.10(360)
0.09x + 64.8 - 0.18x = 36
-0.09x + 64.8 = 36
-0.09x = 36 - 64.8
-0.09x = -28.8
x = -28.8 / -0.09
x = 320
Therefore, you need 320 pounds of cornmeal.
To find the amount of soybean meal, we can subtract the amount of cornmeal from the total mixture weight:
360 - 320 = 40
Therefore, you need 40 pounds of soybean meal.
So, the answer is:
Cornmeal - 320 pounds
Soybean meal - 40 pounds