SOLUTION: I would have tried to answer this question if I knew where to start. Marvelous Marilyn wants to combine a 30% alcohol solution with a 50% alcohol solution to get 500 mg of an 80

Question 32041: I would have tried to answer this question if I knew where to start.
Marvelous Marilyn wants to combine a 30% alcohol solution with a 50% alcohol solution to get 500 mg of an 80% alcohol solution. Please help her accomplish this task.
Please help!
Shakema
Found 2 solutions by Fermat, Earlsdon:
Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
Your question is impossible, as it stands.
There in no way that that you could combine two solutions such that the resulting mixture would have a greater concentration than both the original solutions.
The concentration of the mixture/combination is ALWAYS in between the concentrations of the two original solutions.
The only way to get a greater concentration (without adding another solution of higher concentration) is to boil off some of the water, or in some other way extract it.
You weren't asked this question in order to show that it was impossible, were you?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Well, unless Marvelous Marilyn is also a magician, there is no way for her to obtain a solution of 80% alcohol from a mixture of two alcohol solutions of lesser concentration.
If you give it a little thought, you will see that by mixing a 30% solution with a 50% solution, you can never get a solution that is greater than 50%. Indeed, you will dilute the 50% solution by adding the 30% solution, so you will end up with something in between 30% and 50%. Anyway, just to show you, algebraically, let x = the amount of 30% alcohol solution you will need:
Simplify and solve for x.

Subtract 250 from both sides.
Divide both sides by -0.2

So, you would need -750 mg of 30% alcohol solution and -250 mg of 50% alcohol solution. Doesn't make sense, does it?

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