Personally, I don't use any backing and replace my line at least twice each year on close to 40 reels. Would prefer to have one continuous set of line on the reel. I buy my line in 3000 yard spools and it is cheaper that way.
I seldom use more than 100 yds of main line on any reel... So, using that "rule" I would spool up at least 75 yards of backing. The problem you may encounter is that if your backing is not the same exact diameter as your main line that "175 yds" is meaningless (and even that is based on an unknown assumption about the diameter of some theoretical line at that weight).
Most of my reels are duplicates... So, if I want some semblance of "precision" I spool up backwards (using a Shakespeare clip on line counter, see link below), putting on the desired amount of main line first and "filling the spool" the balance of the capacity with my backer line (usually inexpensive 12 or 20 lb mono) (recording the length of both from the line counter) and then reel this "back" onto the identical reel. I use the recorded numbers to fill the first reel (and any others I want set up the same). (Was that clear?)
About half is line I never change. When putting on new l;ine I strip off wnough where I will never get to the know in normal fishing. Just tie a good knot. In freshwater it is unusual to ever get into the old stuff. Saltwater is a different story. I use 100% fresh good high quality line (and reels) in the salt. You just never know what you will stick out there.