MAT103

Franklin College

Erich Prisner

### Writing Project 27:

# Triangular Mixture Problem

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?