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You are choosing between two different cell phone plans. The first plan charges a rate of 21 cents per minute. The second plan charges a monthly fee of $29.95 plus 8 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable? Round up to the nearest whole minute.

 Dec 14, 2018
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You are choosing between two different cell phone plans.

The first plan charges a rate of 21 cents per minute.

The second plan charges a monthly fee of $29.95 plus 8 cents per minute.

How many minutes would you have to use in a month in order for the second plan to be preferable?

Round up to the nearest whole minute.

 

\(\begin{array}{|rcll|} \hline 21\dfrac{\text{cent}}{\text{minute}}\times x &=& 2995~\text{cent} + 8\dfrac{\text{cent}}{\text{minute}}\times x \\\\ 21\dfrac{\text{cent}}{\text{minute}}\times x -8\dfrac{\text{cent}}{\text{minute}}\times x &=& 2995~\text{cent} \\\\ (21-8)\dfrac{\text{cent}}{\text{minute}}\times x &=& 2995~\text{cent} \\\\ 13\dfrac{\text{cent}}{\text{minute}}\times x &=& 2995~\text{cent} \\\\ x &=& \dfrac{2995~\text{cent}}{13} \cdot \dfrac{\text{minute}}{\text{cent}} \\\\ x &=& \dfrac{2995}{13} ~\text{minutes} \\\\ x &=& 230.38\ldots ~\text{minutes}\\\\ \mathbf{x} & \mathbf{=} & \mathbf{231 ~\text{minutes}} \\ \hline \end{array}\)

 

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 Dec 14, 2018

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