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:______
Here's a previous answer to this problem.
http://www.jiskha.com/display.cgi?id=1252728810
To solve this problem, you can set up a system of equations. Let's represent the pounds of cornmeal as "x" and the pounds of soybean meal as "y."
1. The first equation represents the total weight of the mixture:
x + y = 360 (since the total weight of the mixture is 360 pounds)
2. The second equation represents the protein content of the mixture:
(0.09 * x) + (0.18 * y) = 0.10 * 360
(0.09x) + (0.18y) = 36
To solve this system of equations, you can use either substitution or elimination method. Let's use the elimination method:
Multiply the second equation by 100 to eliminate the decimals:
(0.09x) + (0.18y) = 36
multiply by 100:
9x + 18y = 3600
Now, we have the following system of equations:
x + y = 360
9x + 18y = 3600
To eliminate "y," multiply the first equation by 18:
18x + 18y = 6480
Now, subtract the second equation from the third:
(18x + 18y) - (9x + 18y) = 6480 - 3600
9x = 2880
Divide both sides by 9:
x = 320
Now, substitute this value of "x" into the first equation to find the value of "y":
320 + y = 360
y = 360 - 320
y = 40
So, the mixture should contain 320 pounds of cornmeal and 40 pounds of soybean meal to achieve a 10% protein content.