“Three teas, please,” said the passenger ahead of me in the queue. The Armorique was due in Plymouth any minute, and tea was of the essence.
“That’s £4.65, or €5.60 ((Prices correct as of June 2018)).”
Hang on a moment, I thought, remembering to order my own tea as well. 560 isn’t a multiple of 3. What’s going on?
“That’s £3.10, please, or €3.75.” That’s not even, either!
I didn’t ask - tea, as I mentioned, was of the essence.
It was obvious (to me) that the prices were being calculated in sterling, then converted into euros - but a moment’s calculation suggested that there was also some rounding going on, presumably to the nearest five cents.
If £3.10 is €3.75 to the nearest cent, then - abusing notation slightly - €1.20806… ≤ £1 < €1.21129…
If £4.65 is €5.60, then €1.20323… ≤ £1 < €1.20537…
There is no overlap between the possible exchange rates!
If we’re working to the nearest five cents, then €1.20161… ≤ £1 < €1.21774… from the first piece of information, and €1.19892… ≤ £1 < €1.20968…
Those rates overlap - and we can deduce that the on-board exchange rate is roughly between €1.202… and €1.210… to the pound.
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