If
\[
\frac{x}{2}+1=\frac{y}{4}+4=\frac{z}{3}+2
\quad \text{and} \quad
\frac{x}{16}+\frac{z}{6}=\frac{5}{2},
\]
then \(x+y+z=\)
Show Hint
For expressions of the form
\[
A=B=C,
\]
let each expression be equal to a common variable, express all unknowns in terms of that variable, substitute into the remaining equation, and solve.