Just The Right Amount of Constraints

Algebra Level 3

$\large \begin{cases} a+b+c=50 \\ 3a+b-c=70 \end{cases}$

$a,b$ and $c$ are positive numbers satisfying the system of equations above.

If the range of $5a + 4b + 2c$ is $(m,n)$, what is $m+ n$?

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