Question

A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $30 and then an additional 9 cents per minute of use. In PlanB, the customer pays a monthly fee of $33.60 and then an additional 8 cents per minute of use.For what amounts of monthly phone use will Plan A cost less than Plan B?Use m for the number of minutes of phone use, and solve your Inequality for m.

Answer 1

Let m denote the number of minutes.

Plan A:

The customer pays a monthly fee of $30 and then an additional 9 cents per minute of use.

Mathematically,

`30+0.09m`

Plan B:

The customer pays a monthly fee of $33.60 and then an additional 8 cents per minute of use.

Mathematically,

`33.60+0.08m`

For what amounts of monthly phone use will Plan A cost less than Plan B?

`30+0.09m<33.60+0.08m`

Let us solve the above inequality for m

`\begin{gathered} 30+0.09m<33.60+0.08m \\ 0.09m-0.08m<33.60-30 \\ 0.01m<3.60 \\ m<(3.60)/(0.01) \\ m<360 \end{gathered}`

This means that for less than 360 minutes, plan A will cost less than Plan B.