SOLUTION: Critical Thinking: Without solving, explain what is wrong with the following mixture problem: How many liters of 25% ethanol should be added to 20 liters of 48% ethanol to ob

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Question 512742: Critical Thinking:
Without solving, explain what is wrong with the following mixture problem: How many liters of 25% ethanol should be added to 20 liters of 48% ethanol to obtain a solution of 58% ethanol? Now go through an algebraic solution. What happens?
Found 2 solutions by oberobic, stanbon:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
It is impossible to mix weaker solutions to produce a stronger solution.
If you used entirely 48% solution, the mixture would be only 48%.
If you use any of the 25% solution, the mixture will have to be less than 48%.
Therefore, there is no algebraic solution.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Without solving, explain what is wrong with the following mixture problem: How many liters of 25% ethanol should be added to 20 liters of 48% ethanol to obtain a solution of 58% ethanol? Now go through an algebraic solution. What happens?
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No amounts of 25% and 48% solutions will give you a 58% solution.
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Attempt:
0.25x + 0.48*20 = 0.58(x+20)
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25x + 48*20 = 58x +58*20
-23x = 10*20
x = -200/23 (amt of 25% solution: MEANINGLESS)
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Cheers,
Stan H.
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