Question 206316: Problem:
Soybean meal is 14% protein, cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280-lb mixture that is 13% protein? How many pounds of the cornmeal should be in the mixture? ____pounds.
How many pounds of the soybean meal should be in the mixture? ____pounds.
Thanks
Answer by mickclns(59)   (Show Source):
You can put this solution on YOUR website! Two equations in two variables here, let s be the number of pounds of soymeal in the final product and let c be the number of pounds of cornmeal in the final product (It is valuable to be very clear, precise, unambiguous in stating what your variables, and for your own sake WRITE THOSE DOWN to avoid confusion).
First equation involves the weights in the final mixture:
s + c = 280
Second equation involves the weight of the protein in the soy, the corn, and the mixture.
.14s + .07 c = .13(280)
To solve we could use substitution or elimination. I will show elimination. Here is the first equation with both sides multiplied by 14, followed by the second equation multiplied by 100 (gets rid of the decimals):
14s +14c = 14(280)
14s + 7c = 13(280) Now we subtract the left & right sides of the bottom from the L&R sides of the top
7c = 1(280)
Notice s is eliminated and we have an equation with just c and numbers ... div L&R sides by 7
c = 40 And, since s + c = 280, s = 240.
So the answer is that 40 pounds of cornmeal should be mixed with 240 pounds of soymeal.
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