Question

For her phone service, Elsa pays a monthly fee of $15, and she pays an additional $0.05 Per minute of use. The least she has been charged in a month is $70.25. What are the possible numbers of minutes she has used her phone in a month? Use M for the number of minutes, and solve your inequality for M

Answer 1

Fixed monthly fee = $15

Variable monthly fee = $0.05 per minute

Thus, the total fee in a month is

`\begin{gathered} 15+0.05m \\ \text{where m is the number of minutes used} \end{gathered}`

We are also told that Elsa is charged at least $70.25 in a month

That means $70.25 or more

We have the inequality

`\begin{gathered} 15+0.05m\ge70.25 \\ 0.05m\ge70.25-15 \\ 0.05m\ge55.25 \\ m\ge(55.25)/(0.05) \\ m\ge1105 \end{gathered}`

Thus, we have

`\begin{gathered} m\ge1105 \\ ie\text{ the possible number of minutes she has used her phone in a month are} \\ m\in\mleft\lbrace1105,1106,1107,1108,1109,\ldots\mright\rbrace \end{gathered}`

Writing in equality form, we have

`m\ge1105`