Soy bean 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 12% protein?

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.
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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.
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So, looking back at how much pure stuff we need, we can calculate:
.16*S + .08*(320 -S) = 35.2
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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.
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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
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Add 200 lb of cornmeal and 120 lb of soybean meal to have 320 lb of mixture with 11% protein.