muffler question

[blkbird]

i noticed rattling under my car for a while so i assumed i just needed to tighte something up. WEll when i look under my car i saw that the muffler and inlet pipe i guess ud call it are completely separated-i have an after market flowmaster 40 muffler and it splits into dual exhaust from the muffler-but anyways i think it looks like it could be welded because the pipe is close enough to the tapered part going in to the muffler-i went to midas and they said they couldnt and id need a new muffler and probably should do a catback-installed came to $350-should i do this or seek alternatives like a sleeve maybe? what do u think? thanks