How to work with jointly proportional variables?

Question

Given that x is directly proportional to y and directly proportional to z and inversely proportional to w, if x=4 when (w,y,z)=(6,8,5), what is x when (w,y,z)=(4,10,9)?

This was my working (sorry for images, I’m not comfortable with mathjax yet):

However, this is not correct, how would you approach this and what is wrong with my working?

Answer 1

Instead of writing $k$ separately, write it as,

$$x =k\cdot\frac{yz}{w}$$

as $x$ is proportional to $y$ and $z$ and inversely proportional to $w$ as a whole.

from case $1$,

$$4 = k\frac{8\cdot5}{6}\implies k =\frac{3}{5}$$

Use this in case $2$ to find $x$.