SOLUTION: Soybean meal is 16% protein, cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 11% protein?

Question 495346: Soybean meal is 16% protein, cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 11% protein?
Found 2 solutions by ptaylor, oberobic:
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of soybean meal needed
Then 320-x=amount of cornmeal needed
Now we know that the amount of pure protein that exists before the mixture takes place has to equal the amount of pure protein that exists after the mixture takes place, sooooo:
0.16x+0.08(320-x)=0.11*320
0.16x+25.6-0.08x=35.2 subtract 25.6 from each side
0.08x=9.6
x=120 pounds----amount of soybean meal needed
320-120=200 pounds--amount of cornmeal needed
CK
0.16*120+0.08*200=35.2
19.2+16=35.2
35.2=35.2
Hope this helps----ptaylor
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
For mixture problems you need to keep track of how much "pure" stuff you need.
The result is supposed to be 320 lb that is 11% protein.
That means you need to have 35.2 lb of pure protein. The rest is not protein.
.
To get to 11% you need to mix soybean meal that is 16% protein with cornmeal that is 8% protein.
Let S be the weight of soybean meal.
Logically 320 minus S will be the weight of the cornmeal.
.
So, looking back at how much pure stuff we need, we can calculate:
.16*S + .08*(320 -S) = 35.2
.
Multiply both sides by 100 to eliminate the decimals.
16S + 8(320 -S) = 3520
16S + 2560 -8S = 3520
8S = 3520 - 2560
8S = 960
S = 120 lb of soybean meal
that means you have 320 - 120 = 200 lb of cornmeal.
.
Always check your answer.
200 lb of cornmeal has 8% protein, which = 16 lb.
120 lb of soybean meal has 16% protein, which = 19.2 lb
16 + 19.2 = 35.2 lb of protein
.
Answer:
Add 200 lb of cornmeal and 120 lb of soybean meal to have 320 lb of mixture with 11% protein.
.
Done.
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