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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