Soybean meal is 18% protein; cornmeal is 9% protein. How many pound of each should mixed together in order to get 360-lb mixture that is 13% protein
Start with:
18-13=5 lbs of cornmeal
13-9=4 lbs of soybeanmeal.
Total = 9 lbs.
Percentage of protein = (5*0.18+4*0.09)/(5+4)
= 13%
So for 360 lbs,
weight of cornmean=(360/9)*5=200 lbs
weight of soybeanmeal = (360/9)*4=160 lbs.
By algebra:
Let x=weight of cornmeal
(360-x)=weight of soyabeanmeal
(x*0.09+(360-x))/360 = 0.13
Solve for x (=200 lbs of cornmeal)
and 160 lbs of soyabeanmeal.
To find out how many pounds of soybean meal and cornmeal should be mixed together to obtain a 360-lb mixture that is 13% protein, we can set up a system of equations based on the given information.
Let's denote the weight of soybean meal as "x" pounds and the weight of cornmeal as "y" pounds.
According to the given information, the soybean meal is 18% protein, which means that 0.18x pounds of protein comes from the soybean meal. Similarly, the cornmeal is 9% protein, meaning that 0.09y pounds of protein comes from the cornmeal.
Since the total weight of the mixture is 360 pounds, we can write the first equation:
x + y = 360
Additionally, since we want the mixture to be 13% protein, the amount of protein from the soybean meal and cornmeal combined should be 13% of 360 pounds, or 0.13 * 360 = 46.8 pounds.
Therefore, our second equation is:
0.18x + 0.09y = 46.8
We now have a system of equations:
x + y = 360
0.18x + 0.09y = 46.8
To solve this system, there are multiple methods available: substitution, elimination, or matrices. Here, we will use the method of substitution.
First, solve the first equation for x:
x = 360 - y
Now substitute this value of x into the second equation:
0.18(360 - y) + 0.09y = 46.8
Expand and solve for y:
64.8 - 0.18y + 0.09y = 46.8
-0.09y = 46.8 - 64.8
-0.09y = -18
y = -18 / (-0.09)
y = 200
Now substitute the value of y back into the first equation to find x:
x + 200 = 360
x = 360 - 200
x = 160
Therefore, you would need 160 pounds of soybean meal and 200 pounds of cornmeal to obtain a 360-pound mixture that is 13% protein.