SOLUTION: Please help with solution and how obtained for this question. One printing shop charges $5 plus $0.02 per page and a second shop charges $7 plus $0.015 per page. If _________

SOLUTION: Please help with solution and how obtained for this question. One printing shop charges $5 plus $0.02 per page and a second shop charges $7 plus $0.015 per page. If __________ p

Question 84336This question is from textbook finite mathmatics
: Please help with solution and how obtained for this question.
One printing shop charges $5 plus $0.02 per page and a second shop charges $7 plus $0.015 per page. If __________ pages are printed, the total cost is less for the first printing shop.
A. less than 1500
B. less than 2100
C. less than 400
D. less than 900 This question is from textbook finite mathmatics

Found 2 solutions by tutor_paul, bucky:
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
Set up an inequality as follows:

Where P is the number of pages.
Now, solve for P:

Good Luck,
tutor_paul@yahoo.com
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Begin by writing the equations for the Cost (C) of each printer. The general form of these
equations is based on multiplying the cost per page times the number of pages and adding
to that the fixed cost that you pay regardless of the number of pages.
.
For the first printer, the equation for the Cost (C) and the number of pages (P) is:
.
C = (0.02*P) + 5
.
For the second printer, the equation for the Cost (C) is:
.
C = (0.015*P) + 7
.
The first printer is cheaper for a while. You can tell that because if you have 1 page
printed, the cost at the first printer is $5.02 and the cost at the second printer is
$7.015. However, as you increase the number of pages, the difference in the Cost between
the two printers gets smaller and smaller until at some number of pages the Cost of the
two printers is the same. After that number of pages, the Cost for printing more pages
will be less at Printer 2.
.
You can find the point at which the number of pages make the Cost equal at the two printers.
Do this by solving the two Cost equations simultaneously.
.
The two equations are:
.
C = (0.02*P) + 5
C = (0.015*P) + 7
.
We are trying to find the number of pages (P) that will make the Costs equal. Notice that
if C is the same in both equations then the right side of both equations must be equal
also. So we can say:
.
(0.02*P) + 5 = (0.015*P) + 7
.
To solve this requires collecting the terms that have P on one side of the equation
and the numbers on the other side. You can start by subtracting (0.015*P) from both sides
of the equation. This makes the equation become:
.
(0.02*P) - (0.015*P) + 5 = + 7
.
Next subtract 5 from both sides. This results in:
.
(0.02*P) - (0.015*P) = + 2
.
Then subtract the two terms on the left side to get:
.
0.005*P = 2
.
Finally, solve for P by dividing both sides by 0.005, the multiplier of P. The solution
for P is:
.
P = 2/0.005 = 400
.
So if you have 400 pages to print, the Cost should be equal at the two printers. Check this
out.
.
The Cost at the first printer would be $5.00 plus 2 cents a page for the 400 pages
which is 800 cents or $8.00. So the total cost is $5 + $8 = $13.
.
The Cost at the second printer would be $7.00 plus 1.5 cents a page for 400 pages
which is 600 cents or $6.00. That makes the the total Cost $7 + $6 = $13.
.
Since the Cost is $13 at each printer for 400 pages, you can draw the following conclusion:
.
For less than 400 pages, it will be cheaper to use the first printer. At 400 pages it
doesn't matter which printer you use, the Cost will be the same. For any number of pages
greater than 400, you will save money by using the second printer.
.
Answer C is the correct answer.

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