I thought I would start off taking half then I could pay her for doing some jobs at home if she wants to earn back some cash when she is struggling
WHAT is the point of that!? You are going to give her back HER money in return for her doing chores around your house if she is low on money? She will only be low on money because YOU want to take 50% of her income. How about you start off with 25% & review it?
FWIW I agree with her contributing something, however I think half is harsh, tbh. She isn't earning, she is getting a pittance. Taking a token amount from her is fine, I think but half is just taking the piss.
And to those who said she is using utilities/eating etc....well she was doing that last week and probably pretty much all her life so far, so nothing will actually change in that respect!! They don't suddenly start eating more/costing more just because they aren't at school.
My mother charged me over 50% of my weekly wage at 16. I wasn't spending any more than when I was at school, in fact less because being at work I bought my own lunches! It was costing her NO MORE to have me there, I was happy to contribute, but in her case it was greed. It also meant that I couldn't save money for holidays, going out etc.
Sounds the same here, tbh.