More variables than equations

Algebra Level pending

Let \(r =\dfrac{s}{2}\), \(s=7t\), \(t=2u\), \(u=3v\), \(v= 4w\), \(w=10z\) and \(z\neq 0 \).

Find the value of \(\dfrac{r+s+t+u+v+w}{z^{3}}\).

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