[Math4u] Boots 3-for-2 offer

Just been Christmas shopping and had a bit of an argument with a
friend. In the British chain store, Boots, you can buy certain gifts
and some come with the label: "Buy any 2 and get the 3rd free" (but of
course the one you get free must be the cheapest one).

Now, the situation is this (try to imagine it). We are in the queue,
with 3 presents, each to the value of £8. So in my hand I have £8 £8
£8 worth of presents. (I will pay the shopkeeper £16 and that'll be
fine). However, whilst in the queue, I noticed I hadn't bought a
present for my cousin. It only has to be a small present so it will be
one worth £5. I said "quick, we need to get it now so that we can have
£8 £8 £8 £5 worth of presents and thus get 2 free from the offer". My
friend said "Nah, pay for these now, and then go back in and pay for
the £5 one on its own". I was like "woah, hang on, if we do that, we
won't get the offer of 3 for 2" and she said it doesn't matter as it
will come to the same. We had a big argument and she embarrassed me in
front of customers. Turns out I never got the £5 present anyway. (By
the way, the two free presents would have been worth £5 each).

So, who was right? Was it the same whether I paid for the £5 present
now with the 3 other presents or paid for it afterwards. I'm 99.9%
convinced I'm right but she's sowing doubt into my mind. I reckon,
with my method, I'm paying £29 (£8+£8+£8+£5) and getting the two £5
ones free. With her method, she's paying £21 (£8+£8 and getting an £8
one free --- and then paying for the extra £5 gift separately).

So: She has 4 gifts but paid £21.
I have 6 gifts and paid £29, thus I have the better deal.

She says both methods are the *same* but clearly they're not!?!

Kirk

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