"$pax_$plus" simply creates a string. If $pax is "foo", and $plus is "100", then "$pax_$plus" creates the string "foo_100"

Not at all. It tries to look up the variable $pax_ (since an underscore is valid part of a variable name), and fails (and thus interpolates the empty string for $pax_).

use strict; use warnings; would have caught the problem, and can only be highly recommended to Noverast.