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:______
320
23
To solve this problem, we can use a method called the "mixture" or "alligation" method.
Step 1: Let's assign variables to the unknowns in the problem.
Let's say:
x = pounds of cornmeal
y = pounds of soybean meal
Step 2: Set up two equations based on the given information:
Equation 1: The total weight equation: x + y = 360 (since the total mixture is 360 lbs)
Equation 2: The protein content equation: (0.09)x + (0.18)y = (0.10)(360) (since we want the mixture to have a protein content of 10%)
Step 3: Solve the system of equations.
We can use substitution or elimination method to solve the system. Here, let's solve it using substitution:
From Equation 1, we can express x in terms of y:
x = 360 - y
Substituting this value of x into Equation 2, we get:
(0.09)(360 - y) + (0.18)y = 0.10*360
Simplifying:
32.4 - 0.09y + 0.18y = 36
Combining like terms:
0.09y = 3.6
Dividing both sides by 0.09:
y = 40
Step 4: Substitute the value of y into Equation 1 to find x:
x = 360 - y
x = 360 - 40
x = 320
Therefore, to get a 360-lb mixture that is 10% protein, you would need:
Cornmeal: 320 pounds
Soybean meal: 40 pounds