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.

Part B: How many pages should Sandra fax in a year to justify renting the fax machine? Show your work.

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.

Part B: How many pages should Sandra fax in a year to justify renting the fax machine? Show your work.

anonymous · Answer

Let n be the number of pages she faxes.
For her office machine, each page costs her $0.10. The function for the cost for n number of pages would be$$C_{office}(n) = 0.10n$$
For her rented machine, the base cost is $80. For each page, it costs her $0.06. The function for the cost for her rented machine would be$$C_{rented}(n)=80+0.06n$$

For part A, you simply want the inequality. You have the two functions necessary to write the equation (you want cost of rented to be less than cost of the office fax machine).
For part B, using the inequality you found in part A, find n such at the inequality is true.