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HELP! Can anyone do maths?

Posted: Fri Jul 22, 2005 12:10 pm
by Bobinwales
This is driving me crazy, is there anyone out there who can help?

Three men go to a restaurant for lunch, and the bill comes to £30.00 exactly, so they each put a £10 note onto the table.

As the waiter is on his way to pay the money in, he realises that he has overcharged them, and the bill should have come to only £25, so he returns with five £1 coins.

The men take £1 each, and leave £2 for a tip.

Lunch has now cost 3 x £9 = £27 plus £2 tip = £29. Where has the pound gone to make it the £30 that it actually cost?

HELP! Can anyone do maths?

Posted: Fri Jul 22, 2005 12:59 pm
by Erik_Kowal
No. The cost per person of the lunch (excluding tip) was not £9, but £25/3 = £8.33333

The apparent power of the riddle is solely due to the 'authority effect' of the way it is presented, with the £9 per person cost that is asserted in its concluding wording tending to be accepted without question by its audience, even though the presentation of the facts actually embodies a glaring contradiction: "The bill should have come to only £25"; "Lunch has now cost [...] £27". All of this is merely a set-up for the misleading riddle question, "Where has the pound gone to make it the £30 that it actually cost?", whereas the focus of attention should really be the £2 difference between £25 and £27.

HELP! Can anyone do maths?

Posted: Fri Jul 22, 2005 1:23 pm
by Bobinwales
Thank you very much Erik, even though I now know the answer I have a feeling that pubs all over Wales are going to be arguing about it. It's the sort of question you ask just before you leave!

HELP! Can anyone do maths?

Posted: Sat Jul 30, 2005 12:04 pm
by haro
Decades ago, prices in Swiss restaurants and bars didn't include tips, just as in the USA. Tips of 15% of the amount billed were sort of customary law. Then the umbrella organization of restaurant proprietors announced plans to include 15% for tips in the prices on the menus. That caused an uproar in the unions. Those folks said: A bill of, say, $10.00 according to old system will be $11.50 according to the plans of the proprietors, of which $1.50 have to be be payed to the waitperson. But $1.50 is only 13.04% of $11.50, not 15%, so the staff is better off with the old system.

This is not a joke. It was extensively covered by the media, and of course it was great grist to the mills of all math teachers.

"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." -- Albert Einstein

HELP! Can anyone do maths?

Posted: Tue Aug 23, 2005 7:29 pm
by moon94
So where can i find the origional? :o:?:o

HELP! Can anyone do maths?

Posted: Mon Aug 29, 2005 10:17 am
by Wizard of Oz
Haro you have made the same mistake .. or at least the unions have .. to arrive at their 13.04% they have included the tip and the bill .. the tip is only calculated on the original $10 and not $11.50 .. so the staff are just as well off under either system .. provided of course that you can trust the owners to actually pay up ..

WoZ of Aus 29/08/05

HELP! Can anyone do maths?

Posted: Mon Aug 29, 2005 6:49 pm
by kagriffy
WOZ, you need to re-read Haro's post. He is quoting what the unions representing the wait staff said. I'm assuming (from his comment "This is not a joke") that he understands the distinction. He was simply pointing out another example of a group of people misusing math to "prove" their point.

Sorry, Hans Joerg, I know you could have defended yourself, but I just saw WOZ's post and thought I'd try to clarify your point. Feel free to correct me if I've misstated your intent.

HELP! Can anyone do maths?

Posted: Mon Aug 29, 2005 10:56 pm
by haro
Kagriffy, thanks. Of course you are as right as can be.

WOZ, be glad you wrote, ".. or at least the unions have .." That has saved your face ;-)

HELP! Can anyone do maths?

Posted: Thu Sep 01, 2005 2:09 am
by Wizard of Oz
.. after the number of scrums I have stuck my head into, nothing can save my face .. *crooked grin* ..

HELP! Can anyone do maths?

Posted: Thu Sep 01, 2005 2:27 am
by kagriffy
This whole math issue reminds me of something I witnessed a few years ago. The church I was attending at that time had a day care center, and the day care workers weren't covered by Social Security (because of the tax-exempt status of the church). The church was preparing to "opt in" to Social Security for the employees, which meant the church would start collecting additional taxes from the employees. Because these workers didn't make much more than minimum wage, the church didn't want to harm the employees, so they voted to give each employee a percentage raise equal to the tax rate. I tried to make SOMEONE understand that the employees would actually receive LESS take-home pay, but no one could understand. (Here's a simple example: A worker makes $100 a week, and the tax rate is 10%. If you give him a 10% raise, he then makes $110 a week. Taking 10% of $110, the tax is $11, leaving him with $99 instead of $100.) I guess there are three types of people: those who can do math, and those who can't! *G*

HELP! Can anyone do maths?

Posted: Thu Sep 01, 2005 8:03 am
by Erik_Kowal
Something similar applies in relation to freebie product promotions in a way that makes them sound much better than they actually are.

For instance, if a manufacturer of washing powder plasters the come-on slogan "10% EXTRA FREE!" on a carton that usually contains 100 grams, the carton contents now equal 110 grams. The ratio of consumer-paid-for versus 'free' product is thus 10:1.

If the slogan simply reads "10% FREE!", the ratio of paid-for versus 'free' product is 90 grams versus 10 grams, or 9:1. Result: from the manufacturer's point of view, a less profitable product in a smaller, and hence less impressive-looking, container, and a less impressive-sounding promotional claim.

Which is why no-one ever promotes their products in those terms. And if it comes to that, a similar relationship exists between the related concepts of margin and mark-up: a 10% margin is more profitable (10% profit) than a 10% mark-up (9.09090909...% profit).

Of course, the church employees would have been slightly worse off in the short term under the new arrangement, but would eventually benefit from Social Security (i.e. a State pension) when they retired, which makes your example of loss versus break-even, K, something other than straightforward when one takes the overall context into account.