You have three large 2 liter containers, named A, B, and C, and a small cup of yet unknown volume. At the beginning you have 0.9 liter of 30% acid solution in container B, and 1.2 liter of 50% acid solution in container C. In container A you have 1.2 liter of an acid solution of unknown concentration.
Now we take one cup of the solution in container A and put it into container B, one cup of the resulting solution in container B and put it into container C, and one cup of the resulting solution in container C and put it into container A.
We know that the acid concentration in container A after this procedure is three fourth of its concentration before. Determine the necessary size of the cup used as a function of the concentration of the solution in container A. What is the domain of this function?
Erich Prisner, August 2003