SOLUTION: A farmer needs 120 gallons of 16% nitrogen fertilizer. He only has 12% and 22% nitrogen fertilizers to work with. How much of the 12% and 22% are needed in order to complete the mi

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Question 356356: A farmer needs 120 gallons of 16% nitrogen fertilizer. He only has 12% and 22% nitrogen fertilizers to work with. How much of the 12% and 22% are needed in order to complete the mixture?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the amount of 12% solution, B the amount of 22% solution.
.
.
Total volume equation:
1.A%2BB=120
.
.
Concentration equation:
12A%2B22B=16%28120%29
2.6A%2B11B=960
Multiply eq. 1 by (-6) and add to eq. 2 to eliminate A and solve for B.
-6A-6B%2B6A%2B11B=-720%2B960
5B=240
highlight%28B=48%29gallons
Then from eq. 1,
A%2B48=120
highlight%28A=72%29gallons