I don't think you can calculate bill splits in the way you're implying - it's both too complex to do realistically and too transactional.
At those ages and you're happy to pay half for the 12yo, it's either:
Treat as 4 people, you pay 1.5, wife pays 2.5, so percentage wise: You 37.5, wife 62.5%,
Or
Treat as 3 adults, you pay one, wife pays two, so 33.4% & 66.6%.
That assumes you're earning roughly equal though. Otherwise there's a whole different conversation about what's fair in terms of relative splits from income, and how much each person has left for themselves...
And separate to the above, you need to have a conversation with your wife about how she's going to give the 19yo more responsibilities, insist that he contributes to the household fully, even if not financially, and encourage him to either go into studying or employment, with a backstop that neither is not an acceptable answer.