Question

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)

Answer 1

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 $