Question 467637: I'm having some difficulties solving mixture word problems, more in the area of creating a table. Any advice would be greatly appreciated.
Here the problem!
Suppose that a chemist is mixing two acid solutions, one of 20% concentration and the other 30% concentration. Which one of the following concentrations could not be obtained?
A. 22% B. 24% C. 28% D. 32%
I tried to setup a table as the one listed below
{Acid Amount} {Concentration Amount} {Total of A&C Amount}
20& of solution| x .2 .2(x)
30% of solution| x .3 .3(x)
Mixture |
I'm lost because it does not advise the total amount of concentration that is needed, therefore I do not know what to enter for mixutre. My equation will end up looking like this.
.2x + .3(X) = ?
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! this is more of a thought solution than a calculation
if your mixing a stronger solution with a weaker one, how could you get a mixture that is weaker than the weakest component?
similarly, how could you get a mixture that is stronger than the strongest component?
for a numerical insight, pick any mixture amount ___ like 100ml
.2(x) + .3(100 - x) = .32(100)
.2x + 30 - .3x = 32
-.1x = 2 ___ x = -20 ___ this negative value is not realistic
___ what it is telling you is that mixing 20ml of 20% with 100ml of 32% will give you 120ml of 30%
the bottom line is that the concentration of any mixture is somewhere between the strongest and weakest components
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