jmc

If $n$ is the number of coins in Paula's purse, then their total value is $20n$ cents. If she had one more quarter, she would have $n+1$ coins whose total value in cents could be expressed both as $20n+25$ and as $21(n+1)$. Therefore $$20n+25=21(n+1),\text{so}n=4.$$Since Paula has four coins with a total value of 80 cents, she must have three quarters and one nickel, so the number of dimes is $\boxed{0}$.