G10.3 If $k=\frac{3 \sin \theta+5 \cos \theta}{2 \sin \theta+\cos \theta}$ and $\tan \theta=3$, find $k$.
$\begin{aligned} k & =\frac{(3 \sin \theta+5 \cos \theta) \div \cos \theta}{(2 \sin \theta+\cos \theta) \div \cos \theta} \\ & =\frac{3 \tan \theta+5}{2 \tan \theta+1} \\ & =\frac{3 \times 3+5}{2 \times 3+1}=2\end{aligned}$