SOLUTION: a fertilizer manufacturer has two fertilizers, one which contains 24% nitrogen, and the other contains 16% nitrogen. How much of each fertilizer should be mixed together to make 5

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Question 726866: a fertilizer manufacturer has two fertilizers, one which contains 24% nitrogen, and the other contains 16% nitrogen. How much of each fertilizer should be mixed together to make 500 pounds of a fertilizer that is 21% nitrogen?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = lbs of 24% fertilizer
Let y = lbs of 16% fertilizer
Known:
1) x is 24% nitrogen
2) y is 16% nitrogen
3) Mixture is 21% nitrogen
4) total weight is 500lb
Equations:
(1) x + y = 500
(2) .24x + .16y = .21*500
Solve (1) for x and get
(3) x = 500 - y
Now substitute (3) into (2) to get
(4) .24*(500-y) + .16y = 105 or
(5) 120 - .24y + .16y = 105 or
(6) 0.08y = 15 or
(7) y = 15/0.08 or
(8) y = 187.5
From (3) we get
(9) x = 500 - 187.5 or
(10) x = 312.5
Let's check with (2).
Is (.24*312.5 + .16*187.5 = .21*500)?
Is (75 + 30 = 105)?
Is (105 = 105)? Yes
Answer:Mix 312.5lbs of 24% nitrogen fertilizer and 187.5lbs of 16% nitrogen fertilizer to get 500 lbs of 21% nitrogen fertilizer.