You are choosing between two different cell phone plans. The first plan charges a rate of 25 cents per minute. The second plan charges a monthly fee of $49.95 p

Question

You are choosing between two different cell phone plans. The first plan charges a rate of 25 cents per minute. The second plan charges a monthly fee of $49.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable? Round your answer to the nearest minute

Answer 1

Let's say number of minutes used in a month = m

 

Based on this,

plan A will cost 25 cents(m) = $0.25(m) = 0.25m

plan B will cost $49.95 + 11 cents(m) = $49.95 + $0.11m

 

In order for plan B to be cheaper than plan A, the following inequality must hold true.

cost of plan A > cost of plan B

0.25m > 49.95 + 0.11m

 

Subtract 0.11m from both sides to get

0.14m > 49.95

 

Now, divide both sides by 0.14 to get
m > 356.79

Thus, the smallest possible integer value of m for which plan B is cheaper than plan A is 357 i.e. 357 minutes.