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monthly fees = $13
Additional fees = $0.05 per minute
The least she has been charged in a month = $77.35
number of minutes = m
Therefore,
[tex]\begin{gathered} 13+0.05m\ge77.35 \\ 0.05m\ge77.35-13 \\ 0.05m\ge64.35 \\ m\ge\frac{64.35}{0.05} \\ m\ge1287\text{ minutes} \end{gathered}[/tex]