Berechne die Variable

Berechne die Variable!

6:y:8=15:5:(z+3)

$\begin{array}{|rcrcrcrcrcr|} \hline 6 & : & y & : & 8 & \qquad = \qquad & 15 & : & 5 & : & (z+3) \\ \downarrow & & \uparrow & & & & \downarrow & & \uparrow & & \\ 6& \cdot {\color{red} \left( \frac{y}{6}\right) }& = y & & & & 15& \cdot {\color{red} \left( \frac{y}{6}\right) }& = 5 \\ \\ & & & & & & & 15\cdot \frac{y}{6} = 5 \\ & & & & & & & y = \frac{5\cdot 6}{15} \\ & & & & & & & y = \frac{30}{15} \\ & & & & & & & y = 2 \\ \hline \end{array}$

$\begin{array}{|rcrcrcrcrcr|} \hline 6 & : & y & : & 8 & \qquad = \qquad & 15 & : & 5 & : & (z+3) \\ \downarrow & & & & \uparrow & & \downarrow & & & & \uparrow \\ 6& & \cdot {\color{red} \left( \frac{8}{6}\right) } & & = 8 & & 15& & \cdot {\color{red} \left( \frac{8}{6}\right) } & & = z+3 \\ \\ & & & & & & & & 15\cdot \frac{8}{6} = z+3 \\ & & & & & & & & z = \frac{15\cdot 8}{6}-3 \\ & & & & & & & & z = 20 - 3 \\ & & & & & & & & z = 17 \\ \hline \end{array}$