I'm not aware of any page counter capabilities or software but if there is that's good but what is being printed needs to be put into perspective especially if he's getting only about "10" prints per color ink cartridge.
Since this is for a school I can see many possibilities
It would be good if we knew what "10" prints per color ink cartridge means
--- If he is using HP 58 Photo Inkjet Print Cartridge, HP records it can handle approximately 140 photos
------ Depending on what's being printed (size, amount of solid colors, banners), I can certainly see that estimated amount dropping to to 70 photos easily enough
--- If he is using Tri-Color Inkjet Print Cartridge, the estimated usage is for approximately 165 pages
What needs to be determined is what is being printed: have you seen what is typically being printed?
--- At the office I volunteer at some people had been using up their color cartridges similarly to your input
--- However, when I saw how some prints included solid color backgrounds on a full sheet of paper it was easy to see why that was happening
--- I also saw many heavy duty powerpoints being printed
--- In summary, I suspect a school would have more usage than what I saw
Also depending on what kind of quality color printing is required, normal print v best print setting makes a difference
--- You could set up your own test for what is typically printed
--- The next time a new cartridge is installed, count enough paper or photo paper for "10-20 prints" and check the results