Mistwell
Crusty Old Meatwad (he/him)
Family said:"This is an abstraction; your character probably doesn’t walk into a store one day with a bag of coins, unless you just came into an inheritance or won a tournament of some sort. Rather, the items you start with, and any gold you have left over, might come your way as gifts from family, gear used during military service, equipment issued by a patron, or even something you made yourself." -Equipment, pg 210 PHB
So minus that 50 from your 100. I built an eladrin wizard lately and with the spellbook, orb, armor, SAK, and longsword he had 18g left over.
I do not find your quote to be compelling evidence that you must pay for your spellbook. That it's an abstraction, that your character "might" come your way as gifts from family etc. isn't persuasive to me that the class feature of Spellbook gets subtracted.