SOLUTION: There’re three brand of fertilizers A, B, and C. Following is a table of the amount of nitrogen, phosphorus,
and potassium in a box of each brand (in lb).
Brand A B C
N 1 2
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-> SOLUTION: There’re three brand of fertilizers A, B, and C. Following is a table of the amount of nitrogen, phosphorus,
and potassium in a box of each brand (in lb).
Brand A B C
N 1 2
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Question 607291: There’re three brand of fertilizers A, B, and C. Following is a table of the amount of nitrogen, phosphorus,
and potassium in a box of each brand (in lb).
Brand A B C
N 1 2 2
P 2 1 2
K 2 2 1
How many boxes of each brand are needed in order to make a mixture that contains 6 lb of nitrogen, 6 lb of phosphorus and 7 lb of potassium?
You can put this solution on YOUR website! Set your variables:
a = boxes of A
b = boxes of B
c = boxes of C
You will get three equations:
1: For N: a + 2b + 2c = 6
2: For P: 2a + b + 2c = 6
3: For K: 2a + 2b + c = 7
Solve using determinants, if you have studied them. Otherwise solve by elimination of variables:
Subtract the second equation from the first:
-a + b = 0
So a=b.
..
Substitute b = a into Eq. 1: 3a + 2c = 6
Substitute b = a into Eq. 3: 4a + c = 7
Solve these together for a = 8/3; c = 3/5.
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