In $\triangle ABC$, $DE \parallel BC$. If $AD = 3$, $DB = 5$, $AE = 6$, then $EC = ?$

By the proportionality theorem, $\frac{AD}{DB}=\frac{AE}{EC}$, so $\frac{3}{5}=\frac{6}{EC}$. Cross-multiplying gives $3\,EC=30$, hence $EC=10$.