Owen had some fifty-cent and one-dollar coins.$$ \frac{2}{7} $$ of his coins were fifty-cents coins. His mother gave him $$10$$ one-dollar coins and five-dollars\textquotesingle{} worth of fifty-cent coins. In the end, he had twice as many one-dollar coins as fifty-cent coins. How many coins did Owen have at first? 
Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle