SOLUTION: Soybean meal is 12% protein; cornmeal is 6% protein.? How many pounds of each should be mixed together in order to get a 240-lb mixture that is 80% protein?

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Question 617154: Soybean meal is 12% protein; cornmeal is 6% protein.?
How many pounds of each should be mixed together in order to get a 240-lb mixture that is 80% protein?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
*** note: there is no way you can get 80% protein from
the mixture. I changed it to 8%, which I think is
what you meant ***
Let +a+ = pounds of soybean meal needed
Let +b+ = pounds of cornmeal needed
+.12a+ = pounds of protein in soybean meal
+.06b+ = pounds of protein in cornmeal
----------------
(1) +a+%2B+b+=+240+
(2) +%28+.12a+%2B+.06b+%29+%2F+240+=+.08+
--------------------------
(2) +.12a+%2B+.06b+=+19.2+
(2) +12a+%2B+6b+=+1920+
(2) +2a+%2B+b+=+320+
Subtract (1) from (2)
(2) +2a+%2B+b+=+320+
(1) +-a+-+b+=+-240+
+a+=+80+
and, since
(1) +a+%2B+b+=+240+
(1) +80+%2B+b+=+240+
(1) +b+=+160+
80 pounds of soybean meal is needed
160 pounds of cornmeal is needed
check:
(2) +%28+.12%2A80+%2B+.06%2A160+%29+%2F+240+=+.08+
(2) +%28+9.6+%2B+9.6+%29+%2F+240+=+.08+
(2) +19.2+%2F+240+=+.08+
(2) +19.2+=+19.2+
OK