If the value of $20$ quarters and $10$ dimes equals the value of $10$ quarters and $n$ dimes, then $n=$
$\text{(A)}\ 10 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 35 \qquad \text{(E)}\ 45$
We have 
\begin{align*} 20(25)+10(10) &= 10(25)+n(10) \\ 600 &= 250+10n \\ 35 &= n \implies \boxed{\text{D}} \end{align*}


The  $n$ dimes' values need to sum to $10$ quarters and $10$ dimes.\[10n=10\cdot25 + 10\cdot 10\] we can divide both sides by $10$.
\[n=25+10=35\]
So, our answer is $\boxed{\text{D}}$----stjwyl