Owen had some fifty-cent and one-dollar coins. $\frac{2}{7}$ of his coins were fifty-cent 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