The ratio of the number of marbles Ryan had to the number of marbles Audrey had at first was $$2$$: $$7$$. After Ryan bought another $$20$$ marbles and Audrey gave away $$80$$ marbles, the ratio of the number of marbles Ryan had to the number of marbles Audrey had became $$1$$: $$3$$. How many marbles did Audrey have at first? 
Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle