The answer to a problem is its solution. It is in that sense that one solves a problem ... one melts it in liquid, I guess. A problem with a solution is soluble, just like sugar is soluble in coffee. I think it all comes down from the Latin where resolvere meant something like loosen or untie or dissolve or maybe even melt.

P.S. The Big Boys will weigh in soon with all the heavy references and we will learn much more together.