Question 24
Four positive integers $x,y,z$ and $w$ satisfy the following equations:
$$\begin{aligned}xy+x+y&=104,\\yz+y+z&=146,\\zw+z+w&=524.\end{aligned}$$
If the product $xyzw=2^7\times3^2\times5\times7$, find the value of $x+y+z+w$.
$$\begin{aligned}xy+x+y&=104,\\yz+y+z&=146,\\zw+z+w&=524.\end{aligned}$$
If the product $xyzw=2^7\times3^2\times5\times7$, find the value of $x+y+z+w$.