SOLUTION: a chemist has 2 solutions of HNO3. one has 40% concentrated and the other has 23% concentration. how many liters of each solution must be mixed to obtain 121 liters of a 29% soluti

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Question 786696: a chemist has 2 solutions of HNO3. one has 40% concentrated and the other has 23% concentration. how many liters of each solution must be mixed to obtain 121 liters of a 29% solution?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
I get some funny numbers, but I think I'm right.
Let x = number of liters at a 40% concentrate.
Let y = number of liters at a 23% concentrate.
Then we have
(1) x + y = 121
and
(2) 0.40x + 0.23y = 0.29*121
Multiply both sides of (2) by 100 to get
(3) 40*x + 23*y = 29*121
Solve (1) for x and put into (3) to get
(4) 40*(121 - y) + 23*y = 29*121 or
(5) 40*121 - 40*y + 23*y = 29*121 or
(6) -17*y = (29 - 40)*121 or
(7) y = 11*121/17
Then from (1) we get
(8) x = 121 - 11*121/17 or
(9) x = 6*121/17
Let's check this with (2).
Is (0.40*6*121/17 + 0.23*11*121/17 = 0.29*121)?
Is (2.4*121/17 + 2.53*121/17 = 0.29*121)?
Is (4.93*121/17 = 0.29*121)?
Is (0.29*121 = 0.29*121)? Yes
Answer: Use about 42.7 liters of the 40% concentrate and about 78.3 liters of the 23% concentrate of HNO3 to get 121 liters at a 29% concentration.