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. (5 points)

Part B: How many pages should Emily print in a year to justify renting the photocopier? Show your work. (5 points)

Answer 1

Please NAME the number of pages per year. Seriously, just give it a name.

Answer 2

She uses some number of pages, right?

Answer 3

Shall we refer to that number of pages as "the number of pages she uses" or shall we make a more obvious name, so we can talk about it?

Answer 4

P for pages

Answer 5

p=number of pages. so the inequality would be 0.08=90+0.03?

Answer 6

Can you now write an expression for the total cost of copies, given P pages, and using the college photocopier?

Answer 7

p = # of pages

.08p > 90 + .03p -- this is part A

.08p > 90 + .03p -- subtract .03p from both sides
.08p - .03p > 90
.05p > 90 -- divide both sides by .05
p > 90/.05
p > 1800

check...
lets let p = 2000

.08(2000) > 90 + .03(2000)
160 > 90 + 60
160 > 150 (correct)

as you can see, she would have to print over 1800 pages to make the rented machine worth her while

Answer 8

Okay, can you now write an expression for the total cost of copies, given p pages, and using the college photocopier?

Answer 9

College Copier

.08/page

Nothing to do with $90
Nothing to do with 0.03/page

The cost for all the pages, using the college copier is "0.08p". We're ONLY talking about the one copier. You keep trying to throw in the other copier. Keep them separate and organized.

Rented Copier.

Nothing to do with 0.08/copy.

The cost for all the pages, using the rented copier is "90 + 0.03p".

This needs to make sense.

Answer 10

So would you divide 0.03 and 90?

Answer 11

sorry i forgot about u : (

Answer 12

r greater understanding, simply ignore one case or the other. (Just long enough to understand. I promise, we'll get back to it, later.)

I ask, how much will it cost to run the college copier for a year. You say, 0.08p. Done.

I ask, how much will it cost to run the rented copier for a year. You say, 90.00 + 0.03p. Done.

Answer 13

Now, we are ready to answer Part B.

Rephrased, what number of pages, or what value of p, will make these two expressions have the same value? Can you answer it?

Answer 14

Let the notation help you. We went to teh trouble to write those two expression for a reason.

IF we are indifferent to the two options, the cost would be the same. In the language of our algebra, that is this:

0.08p = 90.00 + 0.03p

1) Do you see that this is so?
2) Can you solve it? We need a nice value for p.

Answer 15

Now does any of this help in anyway?

Answer 16

so you would subtract 0.03 from both sides?

Answer 17

yes

Answer 18

So you get -0.05 then divide that by 90?

Answer 19

yes

Answer 20

u dont get negative

Answer 21

u get 0.05

Answer 22

Thank You! You helped alot!

Answer 23

your welcome : )