SOLUTION: soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed to get a 350 lb mixture that is 12% protein. Please explain with a table if possi

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed to get a 350 lb mixture that is 12% protein. Please explain with a table if possi      Log On

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Question 665218: soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed to get a 350 lb mixture that is 12% protein. Please explain with a table if possible
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The way I do it is to solve it in a straightforward way,
and then I can build any kind of table I want
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Let +a+ = pounds of soybean meal needed
Let +b+ = pounds of corn meal needed
+.16a+ = pounds of protein in +a+ pounds of soybean meal
+.09b+ = pounds of protein in +b+ pounds of cornmeal
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(1) +a+%2B+b+=+350+
(2) +%28+.16a+%2B+.09b+%29+%2F+350+=+.12+
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(2) +.16a+%2B+.09b+=+.12%2A350+
(2) +.16a+%2B+.09b+=+42+
(2) +16a+%2B+9b+=+4200+
Multiply both sides of (1) by 9 and
subtract (1) from (2)
(2) +16a+%2B+9b+=+4200+
(1) +-9a+-+9b+=+-3150+
+7a+=+1050+
+a+=+150++
and, since
(1) +a+%2B+b+=+350+
(1) +150+%2B+b+=+350+
(1) +b+=+200+
150 pounds of soybean meal are needed
200 pounds of corn meal are needed
check answer:
(2) +%28+.16%2A150+%2B+.09%2A200+%29+%2F+350+=+.12+
(2) +%28+24+%2B+18+%29+%2F+350+=+.12+
(2) +42+%2F+350+=+.12+
(2) +42+=+.12%2A350+
(2) +42+=+42+
OK- now you can make a table