# Dear Sorbent

Hi, Sorbent.

How are you? This morning I was in my bathroom and couldn’t help but read the advertising spiel on the back of the plastic wrapping on the rolls of toilet paper. For reference, here’s what it says:

“Always soft, always strong. What makes Sorbent so soft, yet still so strong? It’s a very clever combination of two different types of paper. The top layer is air-dried for softness and thickness, the bottom layer (no pun intended!) is thick creped paper, for added strength. And Sorbent Long Roll means 50% more sheets on every roll. Which means you only need to change it half as often!”

Let’s talk about the last two sentences there. If a Sorbent Long Roll has 50% more sheets on every roll, then you need to change it two-thirds as often, not half as often.

I know you are a toilet paper company, and not the Australian Bureau of Statistics. But I feel that this sort of dishonest marketing may have just been an honest mistake, so I’ll explain it for you.

Let’s suppose a regular roll has 100 sheets, and I use on average 5 sheets per day. This means you would expect me to replace the roll after 20 days (20 days = 100 sheets / 5 sheets per day).

If a Long Roll has 50% more, then it has 100 sheets + 50% of 100 sheets = 150 sheets total. Cool! But I’m still using 5 sheets per day. Therefore I will change the roll after 150 sheets / 5 sheets per day = 30 days.

In 60 days time, I will have used three regular rolls of 100 sheets, or two Long Rolls of 150 sheets. That means I’m replacing the Long Rolls two-thirds as often as the regular ones.

To replace the rolls half as often, each roll would need to be twice as long, i.e. have 100% more sheets, not 50% more sheets.

Note that you can swap out the size of a regular roll and the rate of use, and the maths still works out (as long as you’re consistent)—a Long Roll, if it has 50% more sheets than a regular roll, will be replaced two-thirds as often.

Other than to have even bigger rolls, the only way I can see to get long rolls replaced half as often as regular rolls would be to have reusable toilet paper, and nobody wants that.

In reality, we don’t use toilet sheets at a fixed rate, so your mileage may vary (no pun intended). But I would contend hypothetically that the availability of more toilet paper would encourage people to use it more quickly. This means in practice that Long Rolls get replaced even more often than two-thirds as often as regular rolls.

I realise that this highly advanced analysis using basic arithmetic may be confusing to you, but fortunately you should be able to confirm my working by asking the average third year primary school student. However, please note that to maintain accuracy, you may wish to ask them before the Abbott government brings in yet more national curriculum changes.

Regards,

Josh

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