How to distribute utility bill in a single family home? (House hacking)

[Jonathan Baptiste]

I am currently house hacking and have a few tenants/roommates living with me. I currently pay the water and internet bill out of pocket and only request rent and the electric bill be paid for by the tenants. My house is wired with only one meter so I cannot get a more specific consumption amount for each tenant (even though there is an efficiency unit). Given this limited position the utility bill is split evenly across the tenant as this is the only equitable solution I can think of at the time. I have a comprehensive lease with all my tenants that states they must pay for utilities but not specifically that it will be divided exactly like this. 

A newer tenant (lives in efficiency unit) is displeased with this set up and is voicing this after notifying them of the first utility payment bill. I explained to them my limitations and approach but they threaten to not pay because they do not believe the bill reflects their usage. I am open to an alternative solution but they seem like they using intimidation tactic via email like call my strategy theft (something I take offense to) and that they will not pay and I should figure out the impossible. I do want to work with them but their attitude is making me feel disrespected. 

How would you handle this?