1. ## 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!

2. Half of 23 = 11.5 : is there a half-printer in this organization?

3. 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.

4. 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!

5. 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.