# More Quantitative Confusion

I’m pretty sure printer ink is a huge scam to begin with, and stuff like this doesn’t help.

I went to purchase some ink and looking to minimize my time spent in office supplies stores, I thought I’d buy a two-pack.  “We’re out of the two-pack,” the helpful employee said, “but this is the XL.  It’s the same price as the two-pack, and it has 3 times as much ink as the single cartridge.”

So after my purchase, I felt compelled to perform a side-by-side comparison.

I’d estimate the XL cartridge to be about 120% the size of the original.  But its ink capacity is 350% of the original?  That doesn’t seem to add up.

#### patrick honner

Math teacher in Brooklyn, New York

#### David Radcliffe · January 22, 2012 at 8:42 pm

HP estimates that the 74 cartridge can print 200 pages and the 74XL cartridge can print 750 pages. Perhaps there is not a simple linear relationship between the amount of ink in a cartridge and the number of pages that can be printed.

#### MrHonner · January 22, 2012 at 8:54 pm

An interesting hypothesis, although it’s hard for me to imagine why the relationship wouldn’t be linear.

#### Sam Kolins · January 22, 2012 at 9:46 pm

I would figure that the lack of linearity there is due to the fact that there are bound to be pages that one must print that require much more ink than what is considered average (for examples, pages with pictures or diagrams or tables on them).

#### MrHonner · January 22, 2012 at 10:12 pm

That’s certainly true, but that will affect all cartridge types equally. David is suggesting something different: that doubling the amount of the ink in the cartridge, say, may not double the number of pages you can print.

#### Jack · January 28, 2012 at 7:46 pm

the amount of ink inside the cartridge of the xl might be 350% the amount in the reg cartridge. the cartridge size might just to there to throw ppl off.

#### Sean Wilkinson · December 7, 2012 at 7:38 pm

I think a lot of the space inside is taken up by some kind of filter, which would be the same size in both models.

Mildly interesting math problem: assuming the salesperson is not full of BS, how big is the filter?

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