Question 204889: 5. 5. A 200 lb batch of feed is being formulated using corn, dried distiller’s grain (DDGs) and soybean meal. The corn is 6.5% crude protein and the soybean meal is 45% crude protein. Dried distiller’s grain is 27% crude protein. The final diet should be 15% crude protein. The final diet will include 20 lbs of DDGs. How much corn and soybean meal should be added to mix this batch of feed?
(HINT: Take x to be lbs of corn, y to be lbs of soybean meal, z to be lbs of DDGs. You already know what one of these should be.)
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! OK, We'll use your hint (sort of)
Let x=lbs of corn needed
We are told that 20 lb=lbs of DDGs needed
Then 200-(x+20)=200-x-20=
180-x=lbs of soybean meal needed
Now we know that the amount of pure crude protein before they are mixed together
(0.065x+0.27*20+0.45(180-x)) has to equal the amount of pure crude protein after they are mixed together (0.15*200), so our equation to solve is:
0.065x+0.27*20+0.45(180-x)=0.15*200 simplify
0.065x+5.4+81-0.45x=30 collect like terms
-0.385x+86.4=30 subtract 86.4 from each side
-0.385x=-56.4 dibvide each side by -0.385
x=146.5------------------------lbs of corn needed
20-----------------------------lbs of DDGs neede
180-x=180-146.5=33.5-----------lbs of soybean meal needed
CK
0.065*146.5 + 0.27*20 + 0.45*33.5=0.15*200
9.5225 + 5.4 + 15.075=30
~~~~30=30
Hope this helps---ptaylor
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