PositiveReals puts a constraint on every variable. A notebooks is attached with code.

Attachments:

solve.nb

Frank,

The reason Solve fails is that you have more variables in the equations than you told Solve about. This works (by adding res to the list of variables):

Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, 
  b > 0}, {a, b, k, res}]

as does this (let Solve figure out the variables):

Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, 
  b > 0}]

However, the minimize approach runs faster if you know that the minimum is the solution.

Regards,

Neil