Question

To own and operate a home printer, it costs $100 for the printer and an additional $0.05 per page for ink. To print out pages at an office store, it costs $0.25 per page. Let p represent number of pages.
(1) For the costs to be the same, how many pages do you need to print?
(2) How much does it cost to print that many pages?

Answer 1

Answer: (1) You would need to print 500 pages

(2) To print 500 pages from home would cost $125

Step-by-step explanation: The cost of printing at home has been given as a fixed cost of 100 plus an additional variable cost of 0.05 per page for ink, that is, Cost = 100 + 0.05p. Also, to print at the office, the cost has been given as 0.25 per page, that is, Cost = 0.25p.

Therefore for the costs to be the same, we need to equate both cost functions (that is, C = C) as follows;

100 + 0.05p = 0.25p

Collect like terms and we now have,

100 = 0.25p - 0.05p

100 = 0.20p

Divide both sides of the equation by 0.2

500 = p

To print 500 pages at home therefore would cost,

C = 100 + 0.05p

C = 100 + 0.05(500)

C = 100 + 25

C = 125

Therefore to print 500 pages from home would cost $125

Answer 2

Answer:

1.) 500 pages

2.) $125

Step-by-step explanation:

Given that the printer cost $100. To operate at home will cost

100 + 0.05P

To print out pages at an office store, it will cost 0.25P

1.) For the costs to be the same, then

100 + 0.05P = 0.25P

0.25P - 0.05P = 100

0.20P = 100

P = 100/0.2

P = 500 pages

500 pages need to be printed

2.) How much does it cost to print that many pages?

Cost = 0.25P

= 0.25 × 500

= 125 dollars