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.

## 2 Replies to “Elegance and clarity”

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I think you will find that you have forgotten to pay interest to S, calculated daily and maybe a couple of a percent above the base rate.

Don’t worry Keith. By a series of startling co-incidences, the interest owed to

Sand others precisely equals the extortionate fee charged byRfor auditing the weekend’s accounts.