Mixture Problems

You know this one too:

Given:

Solution A contains 20% acid

Solution B contains 60% acid

Find: The number of mL of each necessary to obtain 450mL a solution that contains 30% acid.

I usually teach this the same way I do work and rate problems. Find what we call a "guiding equation" that is based on the units available in the problem and set up some sort of table to organize the information. Depending on the given information, we may use two variables and solve a system of equations. Maybe not. But at the end of the day, this is going to be some complex variation of a rate problem.

I have a colleague who sees these problems in terms of proportions and our recent conversations have inspired this GeoGebra applet.



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There may be some rounding error, but I think this gives an interesting conceptual spin to a problem that can very easily become an algorithmic nightmare.

We can make some quick adjustments for the good ol' price per pound problems as well.




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Download % Mixture applet
Download Price per Pound applet