Sandra uses her office fax machine to send fax at the rate of $0.10 per page. she decides to rent a fax machine for $80 a year. the cost of sending a fax using the rented machine is $0.06 per page. part a: write an inequality that can be used to calculate the number of pages that sandra should fax in a year so that the amount she pays for the rented machine is less than the office machine. define the variable used. (5 points) part b: how many pages should sandra fax in a year to justify renting the fax machine? show your work. (5 points)

Part A: 
 First we define the variable to be used for the problem:
 x: the number of pages that Sandra should fax
 The inequality for rent is:
 0.06x <= 80
 Note that the price will be less than using the fax from the office, since for the same number of pages, we have:
 y = 0.10x
 
 an inequality that can be used to calculate the number of pages that Sandra should fax in a year is:
 0.06x <= 80

 Part B:
 0.06x <= 80
 From here we clear x:
 x <= 80 / 0.06
 x <= 1333.33333
 Nearest whole number
 x <= 1333
 Sandra can use the leased fax for 1333 pages and the cost will be:
 1333 * 0.06 = 79.98 $
 Using the office fax the cost will be:
 1333 * 0.1 = 133.3 $
  
 By renting the sara machine, you save:
 133.3-79.98 = 53.32 $