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 Answer: 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 $ Answer: By renting the sara machine, you save: 133.3-79.98 = 53.32 $
