jmc

Let the three basset hounds weigh $a$, $a$, and $b$ pounds, where $a<b$. We have the two equations $$\begin{array}{rl}2a+b& =185\\ b-a& =20\end{array}$$ From the second equation, we have $a=b-20$. Substituting this in to the first equation to eliminate $a$, we have $2(b-20)+b=185\Rightarrow b=75$. Thus, the largest dog weighs $\boxed{75}$ pounds.