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