Question

Your friend needs your help. His parents have told him that it is time for him to start paying for his own cell phone. After completing some research on the internet, you have narrowed down his options. Option 1 charges $0.30 for each cell phone call and $25 for unlimited text messaging. Option 2 charges a flat rate of $40.

Which plan is the best option?​

Answer 1

For less than 50 calls, option 1 is the best, while for more than 50 calls, option 2 is the best.

Explanation:

Option 1:

For n calls, the cost is given by:

`C_(1)(n) = 25 + 0.3n`

Option 2:

The cost is flat of 40, so
`C_(2)(n) = 40`

Which plan is the best option?​

Depends on the number of calls, as for a high number,
`C_1` will be higher than
`C_2`. We have to find this number. So

`C_(1)(n) > C_(2)(n)`

`25 + 0.3n > 40`

`0.3n > 15`

`n > (15)/(0.3)`

`n > 50`

This means that for less than 50 calls, option 1 is the best, while for more than 50 calls, option 2 is the best.