Given: $\frac{x}{x + y}*10 + \frac{y}{x + y}*20 = k$

Rewrite as follows: $\frac{10x}{x + y} + \frac{20y}{x + y} = k$

Rewrite as follows: $(\frac{10x}{x + y} + \frac{10y}{x + y}) + \frac{10y}{x + y}= k$

Simplify: $(\frac{10x + 10y}{x + y}) + \frac{10y}{x + y}= k$

Simplify: $10 + \frac{10y}{x + y}= k$

Rewrite as follows: $10 + 10(\frac{y}{x + y})= k$

IMPORTANT: If $x = y$, then $\frac{y}{x + y} = \frac{y}{y + y} = \frac{y}{2y} = \frac{1}{2}$

Since it's actually the case that $x < y$, then we know that $\frac{1}{2} < \frac{y}{x + y} < 1$, which means $10(\frac{y}{x + y})$ is greater than 5 but less than 10.

So, we know that $15 < k < 20$

Answer: D