SOLUTION: 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 12% protein? How the heck do I obtai

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Question 631963: 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 12% protein?
How the heck do I obtain the results? I understand converting the % to decimals, but now how to set this one up. Help asap is very appreciated.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of soybean meal needed
Let +b+ = pounds of cornmeal needed
+.14a+ = pounds of protein in soybean meal needed
+.07b+ = pounds of protein in cornmeal needed
------------
(1) +a+%2B+b+=+280+
(2) +%28+.14a+%2B+.07b+%29+%2F+280+=+.12+
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(2) +.14a+%2B+.07b+=+.12%2A280+
(2) +.14a+%2B+.07b+=+33.6+
(2) +14a+%2B+7b+=+3360+
(2) +2a+%2B+b+=+480+
-----------------
Subtract (1) from (2)
(2) +2a+%2B+b+=+480+
(1) +-a+-+b+=+-280+
+a+=+200+
and, since
(1) +a+%2B+b+=+280+
(1) +200+%2B+b+=+280+
(1) +b+=+80+
200 pounds of soybean meal are needed
80 pounds of cornmeal are needed
check:
(2) +%28+.14a+%2B+.07b+%29+%2F+280+=+.12+
(2) +%28+.14%2A200+%2B+.07%2A80+%29+%2F+280+=+.12+
(2) +%28+28+%2B+5.6+%29+%2F+280+=+.12+
(2) +33.6+=+.12%2A280+
(2) +33.6+=+33.6+
OK