Question

Sandra uses her office fax machine to send faxes 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. (5 points)

Part B: How many pages should Sandra fax in a year to justify renting the fax machine? Show your work. (5 points) please help me understand this!!!

Answer 1

anyone?

Answer 2

The difference per page .04
in other words, every page she saves $.04 (using rental machine)

so let x represent the number of pages
and 80 dollars the amount that is supposed to be paid off.

.04x>80 <--- that's your equation.

Now we solve...
.04x>80
.04x÷.04>80÷.04
same as (b/c 25 is a multiplicative inverse of .04)
.04x×25=80×25
x>80×25
x>2000

Your final answer for part a is x>2000

Answer 3

Oops I misread the question, I already gave you the part b, it is 2000 or more.
for part a....

So Part A is .04x>80
& Part B is (at least) 2000

Answer 4

her fax machine : 0.10p ---(10 cents per page)
rented machine : 80 + 0.06p ---(80 bucks + 6 cents per page)

it is saying: if rented machine is less..
0.10p > 80 + 0.06p <=== answer for A (variable used (p) stands for # of pages)

0.10p > 80 + 0.06p -- subtract 0.06p from both sides
0.10p - 0.06p > 80
0.04p > 80 -- divide both sides by 0.04
p > 80/0.04
p > 2000

to justify renting the fax machine, she would have to she would have to fax more then 2000 pages.

check...
lets say she faxed 3000 pages...p = 3000
0.10(3000) > 80 + 0.06(3000)
300 > 80 + 180
300 > 260

as you can see, it would cost her $300 for her office machine and it would cost her $260 for the rental.
So basically the number of pages would have to be over 2000 to justify using the rental.