`open -a` results in an "Unable to find application" error on OS X

Have you considered the following?

open -a Numbers

Applications opened by open aren't opened relative to their path, but just according to their actual name, as identified in Contents/Info.plist in the .app file itself.

If you want to be sure, you can also use the Bundle Identifier with the -b option:

open -b com.apple.iTunes

Which can be found in the Info.plist file too: