Elegance and clarity

I really don’t know what all the fuss was about.
Say five people go to a weekend music festival together. At various times during the weekend, they pay for groceries and travel expenses. R pays £3 for margerine, £3 for electricity, totalling £6. L pays £17.50 for some groceries. E spends £10 in the shop and another £2 for some communal painkillers to ease hangovers, a total of £12. K spends £7.50 on groceries and £6 on electricity cards, which totals £13.50. S pays for car hire at £113 for the weekend, then £18 for parking, £15 on petrol, and £54 on groceries, a total of £200 exactly.
That means we’ve spent £249 in total, or £49.80 each.
If S has paid £200 but owes £49.80, she is due £150.20 from the other four. However, K and E foolishly gave her £3 each, and R has already handed over £5 early in the proceedings, so really S only needs £139.20. Since K has already spent £13.50, he should contribute another £36.30, £3 of which he has already paid. £33.30 is still due. Since E has paid £12 already, plus another £3 to S, only £34.80 of her £49.80 share is due. Likewise, L has already paid £17.50 of his equal share, so he still needs to pay £32.30. R has only made purchases of £6, but since he has already paid £5 to S he now owes £38.80 to the group.
Since S is owed money, the other four should pay her back. £139.20 divided by four is £34.80 owed to S by each of the other members. By luck, this is exactly what E owed to the group anyway, so now both S and E are ‘quits’ with the group. This just leaves K, L and R. Since K only owed £33.30 in the first place, his paying over £34.80 to S leaves him £1.50 short. By a similar calculation, L only owed £32.30, so paying £34.80 to S left him £2.50 out of pocket. All is not lost however, because although R owed a total of £38.80 to the group, he only paid S £34.80 of that sum. R therefore has £4 outstanding to the group, which K and L can split between them.
To summarize, everyone pays S £34.80, and R pays supplements of £1.50 to K and £2.50 to L. Simple.

Cartoon by Sidney Harris.
Cartoon by Sidney Harris.

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