smc

We know that $n\le 30$ or else $30-n$ will be negative, resulting in a negative fraction. We also know that $n\ge 15$ or else the fraction's denominator will exceed its numerator making the fraction unable to equal a positive integer value. Substituting all values $n$ from $15$ to $30$ gives us integer values for $n=15,20,24,25,27,28,29$. Counting them up, we have $\boxed{7}$ possible values for $n$.