Soybean milk is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240 pound mixture that is 8% protein?
sybean --- x
cornmeal --- 240-x
solve
.12x + .06(240-x) = .08(240)
To solve this problem, we can use a technique called the method of weighted averages. Let's break down the problem step by step:
Step 1: Define the variables:
Let's assume that x represents the amount (in pounds) of soybean milk to be mixed, and y represents the amount (in pounds) of cornmeal to be mixed.
Step 2: Set up the equation based on protein content:
The protein content is given as a percentage, so we need to convert it to a decimal. 12% protein becomes 0.12, and 6% protein becomes 0.06. Since we're interested in obtaining a 240-pound mixture that is 8% protein, we can set up the equation as follows:
0.12x + 0.06y = 0.08 * 240
Step 3: Simplify the equation:
Simplify both sides of the equation:
0.12x + 0.06y = 19.2
Step 4: Solve the equation:
Now we have a system of equations to solve simultaneously. However, we can simplify the problem by getting rid of the decimals. We can do this by multiplying the entire equation by 100:
12x + 6y = 1920
Step 5: Apply the constraint:
We also know that the total weight of the mixture should be 240 pounds:
x + y = 240
Step 6: Solve the system of equations:
Now we can solve the system of equations using any preferred method. In this case, we will use the substitution method.
From the constraint equation, we can isolate x:
x = 240 - y
Substituting this value into the first equation:
12(240 - y) + 6y = 1920
Expanding and simplifying:
2880 - 12y + 6y = 1920
Combine like terms:
-6y = 1920 - 2880
-6y = -960
Divide by -6:
y = 160
Substituting this value back into the constraint equation:
x = 240 - 160
x = 80
Step 7: Answer the question:
According to the solutions, 80 pounds of soybean milk and 160 pounds of cornmeal should be mixed together in order to obtain a 240-pound mixture that is 8% protein.