Question

You are choosing between two different cell phone plans. The first plan charges a rate of 20 cents per minute. The second plan charges a monthly fee of $39.95 plus 10 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.

Answer 1

The first plan charges 20 cents per minute

Since 1 dollar = 100 cents, then

20/100 = 0.20 dollars

The first plan charges $0.20 per minute

The second plan charges $39.95 plus 10 cents per minute

10/100 = 0.10 dollars

The second plan charges $39.95 plus $0.10 per minute

We need to make the 2nd plan preferable

That means the charge for the 2nd less than the 1st charge

Let the number of minutes = x, then

`\begin{gathered} 1st\rightarrow Ch=0.20x \\ 2nd\rightarrow Ch=39.95+0.10x \end{gathered}`

We will make 2nd Ch < 1st Ch

`39.95+0.10x<0.20x`

Subtract 0.10x from both sides

`\begin{gathered} 39.95+0.10x-0.10x<0.20x-0.1x \\ 39.95<0.10x \end{gathered}`

Divide both sides by 0.10

`\begin{gathered} (39.95)/(0.10)<(0.10x)/(0.10) \\ 399.5399.5 \end{gathered}`

Since the first whole number greater than 399.5 is 400

Then x = 400

You would have to use the 2nd plan for 400 minutes to be preferable