Just The Right Amount of Constraints

Algebra Level 3

{a+b+c=503a+bc=70\large \begin{cases} a+b+c=50 \\ 3a+b-c=70 \end{cases}

a,ba,b and cc are positive numbers satisfying the system of equations above.

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

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