Math problem on comparing printers?

Question

Jacob is trying to decide between two laser printers,one manufactured by Hewlett - Packard,the other by Brother. Both have similar features and warranties, so price is the determining factor. The Hewlett-Packard costs $180 and printing costs are approximately $0.03 per page. The Brother costs $230 and printing costs are approximately $0.01 per page. How many pages need to be printed for the cost of the two printers to be the same?

Answer 1

Write what you know. :)

x = number of pages printed

Given: Hewlett-Packard costs $180 and printing costs are approximately $0.03 per page

HP cost = 180 + 0.03x

Given: The Brother costs $230 and printing costs are approximately $0.01 per page.

Brother cost = 230 + 0.01x

You want to know when HP cost = Brother cost.

180 + 0.03x = 230 + 0.01x

0.03x = 230 + 0.01x - 180

0.03x -  0.01x = 50

0.02x = 50

x = 50/0.02

x = 2500

The cost will be the same if 2500 pages are printed.

Answer 2

let x be the number pf pages to be printed so for the above condition to  hold true

180+0.03x=230+0.01x

0.02x=50

x=50/0.02

x=2500

Answer 3

There is a difference of 2 cents per page. So for there to be a total difference of 1 dollar would need 50 pages (2 cents * 50). The difference in buying price is 50 dollars, so 50 * 50, which is 2500 pages.