3 equations, 3 variables! part 4

\(a,b,c\) are positive integers satisfying the equations

\[\begin{align*} 5a+5b+2ab &= 92 \\ 5b+5c+2bc &= 136 \\ 5c+5a+2ca &= 244 \end{align*}\]

Find \(7a+8b+9c\).

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