# Average Printer Value

• May 20th 2010, 01:47 AM
funismathsdefinitely
Average Printer Value
Hello,

An organisation prints over 240,000 pages per annum. This is done over 23 printers. What does each printer print on average over a year if:

- Half of the printers at 100% capacity
- Quarter of the printers operates at 50% capacity
- Quarter of the printers operates at 25% capacity

Thanks!
• May 20th 2010, 05:26 AM
Wilmer
Half of 23 = 11.5 : is there a half-printer in this organization? (Wondering)
• May 20th 2010, 06:09 AM
funismathsdefinitely
The assumption in the example is that all printers have the same capacity. I am looking for a average figure that each printer would output based on the criteria.

I appreciate that 11.5 printers is not something that exists in real life but it should not effect the calculation of the average pages printed per printer.
• May 20th 2010, 08:16 AM
HallsofIvy
Quote:

Originally Posted by funismathsdefinitely
Hello,

An organisation prints over 240,000 pages per annum. This is done over 23 printers. What does each printer print on average over a year if:

- Half of the printers at 100% capacity
- Quarter of the printers operates at 50% capacity
- Quarter of the printers operates at 25% capacity

Thanks!

Well, Wilmer's complaint that "Half of the printers at 100% capacity" is inmpossible for 23 printers is still valid. I will take it that, in fact, there were printers operating at many different percentages of capacity and this is a "average" value itself.

This is essentially a "weighted" average problem. Let X be the number of pages printed by the printers running at 100% capacity. The the printers at 50% capacity print X/2 pages and those running at 25% capacity print X/4 pages. Let N be the total number of printers. Then N/2 are running at 100% capacity and, together, print XN/2 pages. N/4 are running at 50% capacity and, together, print (X/2)(N/4)= XN/8, pages. N/4 are running at 25% capacity and, together, print (X/4)(N/4)= XN/16 pages.

Putting those all together, XN/2+ Xn/8+ XN/16= 240000.

1/2+ 1/8+ 1/16= 8/16+ 2/16+ 1/16= 11/16 so that says that (11/16)XN= 240000 and so XN= (240000)(16)/11. Calculate that and divide by N= 23 to find X, the average number of pages printed by the printers operating at 100% capacity. Divide that by 2 to find the average number of pages printed by the printers operating at 50% and by 4 to find the average number of pages printed by the printers operating at 25%.

Of course, if you really want a single average for all printers, ignore all of that and just divide 240000 by 23!
• May 20th 2010, 08:33 AM
funismathsdefinitely
Apologies for questionable query but many thanks for your detailed explanation and answer! Greatly appreciated as could not be sure of the answer I had otherwise.
• May 20th 2010, 09:24 AM
Wilmer