Plug the holes.
Basically take the hinges off. Take a drill and bore the holes out so
they are nice and round. (use a small bit) then use the lengths of
rounds wood that they sell at any home center that is a little larger
then the hole you drilled.
Cut of the approprioate length fill the hole with glue, use a mallet to
pop the plug into your hole let it set then you have nice new wood to
screw into.