In a triangle $ABC$ the point $D$ is on $BC$ such that $\overline{BD}=\frac{2}{3}\cdot \overline{BC}$ and the point $E$ is on $AB$ such that $\overline{AE}=\frac{3}{5}\cdot \overline{AB}$.

The lines $AD$ and $CE$ intersect in $S$.

Write $AS$ as a multiple of $AD$ and $CS$ as a multiple of $CE$.

We have a triangle as follows, right?

[![enter image description here](https://i.stack.imgur.com/Dmw3B.jpg)](https://i.stack.imgur.com/Dmw3B.jpg)

But how can we get an information for $AS$ and $CS$ ? Could you give me a hint? Do we maybe use vector operations?

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**EDIT :**

Using vectors we have $$\vec{AS}+\vec{SD}=\vec{AD} \Rightarrow \vec{AS}=\vec{AD}-\vec{SD} \Rightarrow \vec{AS}=\vec{AD}+\vec{DS}$$ Does this help us ? How can we continue?