What were the most minutes used in a single month? What were the least?

Question

A cell phone company charges $60 for an 800-minute monthly plan, plus an additional $1.22 per minute for every minute over 800. if a customer’s bill ranged from a low of $77.16 to a high of $106.86 over a 6-month period, what were the most minutes used in a single month? what were the least?

Answer 1

The customer bill over 6 months was

$77.16 <= BILL <= $106.86

The fixed charge for 800 minutes per month is $60.

The inequality for extra charges is:

$17.16 <= BILL <= $46.86

the extra charge per minute is $1.22 so we can find the number of extra minutes used for each month by dividing the extra charges by $1.22

17.16 / 1.22 = 14.06

46.86 / 1.22 = 38.41

so the most minutes used in a single month is 800 + 38.41 = 838.41

and the least minutes used in a single month is 800 + 14.06 = 814.06