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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Answer:

Add 200 lb of cornmeal and 120 lb of soybean meal to have 320 lb of mixture with 11% protein.