in reply to using a set variable in system or exec

Before I answer your question I shall point you towards unlink which is a perl function for removing files. As for using variables in system the issue is that the variable in question is being interpolated as $date_more_filename (so nothing to do with the function). So what you need to do is delimit the variable name which you can do by surrounding it in curly braces e.g
my $date = "Tuesday the 8th of 2003"; ## note the {} around the variable name print "Today is ${date}\n"; __output__ Today is Tuesday the 8th of 2003
See. perlop for more info on quoting in perl.
HTH

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broquaint