For each long-distance call anywhere in the continental United States, a new phone service will charge users $0.60 per minute for the first 2 minutes and $0.02 per minute for additional minutes in each call. Tom’s current phone service charges $0.10 per minute for all calls, and his calls are never shorter than 7 minutes.
If Tom’s dorm switches to the new phone service, what will happen to the average length of his calls?

Average call Becomes 15 minutes

Step-by-step explanation:

For Tom's Dorm to not run at a loss for switching to the new phone service the Average length of phone calls must not be less than fifteen (15) minutes.

Mathematically,

If he remains on his current phone line, a call of 15 minutes will cost :

= 0.1 * 15 = $1.5

But if he switches to the new phone line and makes a call for 15minutes, the cost will become :

First 2 minutes = 0.6 * 2 = $1.2

Subsequent 13 minutes will cost = 0.02 * 13 = 0.26

Total call for 15minutes on the new phone line = 1.2 + 0.26 = 1.46.

Since the cost became significantly lesser for 15mins when he switches to the new phone line, then the average calls Tom should make should not be less than 15 minutes.

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