What to do with very low offer on an item for sale

Pretty simple: accept, reject or counter-offer

Ignore or say "no."

I always respond. A polite rejection is easy enough.

First, don’t take it personal. Consider the offer may be all that the potential buyer is willing to pay, or all that they have to spend. It may also be a test of your commitment to the price, in which case it could be the start of a negotiation.

One thing I have learned from 25+ years of buying/selling audio gear is that, whichever side you are on (buying or selling), it is a good practice to give yourself a margin of negotiation.  Human nature motivates people to want feel good about their purchases/sales, and sometimes that means giving up a little at either end. Give yourself a little slack when pricing your goods.  Your 10 percent expectation is good, if the item is priced in the appropriate ballpark to begin with. Finally, as mentioned already, you can just say “no”.  Look hard at potential buyers who offer too little because the only thing worse than selling too low, is selling to a problem buyer.