Problem solving approaches often find a path from the givens to the unknown or from the unknown to the givens. This study explores those approaches using written protocols of Navy subjects while solving for the numerical value of an unknown from several knowns and a system of equations. For a subset of the items, solutions require subjects to retain expressions with both literals and numerals. Successful and unsuccessful students were similar in their preference to work backward and to use literals rather than numerals and in the efficacy of their solutions. Students acquired successful solution methods during instruction and used them consistently. (Author)