Chloe has $60$ copper tokens and $90$ iron tokens. There is a booth where Chloe can give $3$ copper tokens and receive in return a silver token and $2$ iron tokens, and another booth where Chloe can give $4$ iron tokens and receive in return a silver token and a copper token. Chloe continues to exchange tokens until no more exchanges are possible. How many silver tokens will Chloe have at the end?