Soybean meal is 12% protein; cornmeal is 6% protein. howmany pounds of each should be mixed together to get a 240 pound mixture that is 8% protein?
Sum of protein constituents=total protein
.12S+.06P=240*(.08)
S + P=240
Those two equations will solve it.
I don't understand the equations I am having a lot of trouble.
well, if
S+P=240, then S=240-P
then
.12S+.06P=240*.08 or
.12(240-P) + .06P=240*.08
solve for P
To solve this problem, we can set up a system of equations. Let's denote the number of pounds of soybean meal as "x" and the number of pounds of cornmeal as "y".
We know that the total mixture weighs 240 pounds, so we have the equation:
x + y = 240
Next, we need to consider the protein content in the mixture. The protein content in the soybean meal is 12% and the protein content in the cornmeal is 6%. Therefore, the amount of protein in the soybean meal is 0.12x and the amount of protein in the cornmeal is 0.06y.
Since we want the final mixture to be 8% protein, we can write another equation:
(0.12x + 0.06y) / 240 = 0.08
Now we have a system of two equations:
x + y = 240
(0.12x + 0.06y) / 240 = 0.08
We can solve this system of equations to find the values of x and y, which represent the number of pounds of soybean meal and cornmeal, respectively.
First, let's simplify the second equation by eliminating the denominator:
0.12x + 0.06y = 0.08 * 240
0.12x + 0.06y = 19.2
We can multiply this equation by 100 to eliminate the decimals:
12x + 6y = 1920
Now we have a system of equations:
x + y = 240
12x + 6y = 1920
We can use any method (substitution, elimination, or matrix methods) to solve this system. Let's use the substitution method:
Rearrange the first equation to solve for x:
x = 240 - y
Substitute this value of x into the second equation:
12(240 - y) + 6y = 1920
2880 - 12y + 6y = 1920
-6y = -960
y = 960 / 6
y = 160
Now that we have the value of y, we can substitute it back into the first equation to solve for x:
x + 160 = 240
x = 240 - 160
x = 80
Therefore, you should mix 80 pounds of soybean meal with 160 pounds of cornmeal to obtain a 240-pound mixture that is 8% protein.