Maximizing the w

Algebra Level 5

Suppose \(w,x,y,z\) satisfy \[\begin{align*}w+x+y+z&=25,\\wx+wy+wz+xy+xz+yz&=2y+2z+193\end{align*}\] The largest possible value of \(w\) can be expressed in lowest terms as \(w_1/w_2\) for some integers \(w_1,w_2>0\). Find \(w_1+w_2\).

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