A set of observations $\{10, 15, 20, 35\}$ has corresponding weights $\{0.15, 0.30, 0.40, 0.15\}$. The weighted median is defined as the element $x_k$ that satisfies both $\sum_{i: x_i \le x_k} w_i \ge 0.5$ and $\sum_{i: x_i \ge x_k} w_i \ge 0.5$. What is the weighted median of this dataset?