My math books had the answers, but never the work for the odd questions, as long as we could show work that would get the answer, we were fine if we looked in the back in order to work backwards.
I would ignore Lucy, if she calles you on doing something, and the teacher reprimands you, admit to doing it, appologize, and move on. I think her tattling is two-fold. 1 to get an 'in' with the teachers, and 2 to feel superior over the other students. If you accept any appropriate blame, the feeling of power is gone.