Emily uses her college photocopier machine to photocopy at the rate of $0.08 per page. She decides to rent a photocopier machine for $90 a year. The cost of photocopying using the rented machine is $0.03 per page.

Part A: Write an inequality that can be used to calculate the number of pages that Emily should photocopy in a year so that the amount she pays for the rented machine is less than the college machine. Define the variable used.

Part B: How many pages should Emily print in a year to justify renting the photocopier? Show your work.

Question

Emily uses her college photocopier machine to photocopy at the rate of $0.08 per page. She decides to rent a photocopier machine for $90 a year. The cost of photocopying using the rented machine is $0.03 per page.

Part A: Write an inequality that can be used to calculate the number of pages that Emily should photocopy in a year so that the amount she pays for the rented machine is less than the college machine. Define the variable used. 

Part B: How many pages should Emily print in a year to justify renting the photocopier? Show your work.

anonymous · Answer

Lets call the number of pages 'p' and the total cost 'c'.

For the first machine we are told that each page costs 8cents. So:

$$c_{1}=0.08p$$

For the second machine we know that each page costs 3cents AND we have to pay the $90 even we we cop zero pages. So:
$$c_{2}=0.03p+90$$

Part A asks us to find the equation so that the second machine is cheaper. This means we want c2 to be less than c1. So:
$$c_{1}>c _{2}$$
$$0.08p>0.03p+90$$
$$0.05p>90$$
$$p>1800$$

This is the answer to Part A, but it also gives us the answer to Part B: "Emily needs to copy more that 1800 pages per year to make machine 2 the cheaper option."