Pizza Investigation Author(s): Lesley Jones Source: Mathematics in School, Vol. 32, No. 2 (Mar., 2003), pp. 19-21 Published by: The Mathematical Association Stable URL: http://www.jstor.org/stable/30215588 . Accessed: 06/10/2013 15:40 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access to Mathematics in School. http://www.jstor.org This content downloaded from 141.161.91.14 on Sun, 6 Oct 2013 15:40:58 PM All use subject to JSTOR Terms and Conditions
Transcript
Pizza InvestigationAuthor(s): Lesley JonesSource: Mathematics in School, Vol. 32, No. 2 (Mar., 2003), pp. 19-21Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30215588 .
Accessed: 06/10/2013 15:40
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp
.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].
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A simple enough event. In an act of uncharacteristic generosity I decided to treat a colleague to a cup of coffee and so ordered two cups instead of my usual one. "That will be a1.41, please", stated the smiling cashier. Money duly changed hands and we settled down to drink the coffee in the enjoyable surroundings of the staff canteen.
But something wasn't quite right - my one cup of coffee normally costs 71p. Why was the second one cheaper? Was there a secret promotional campaign to boost sales by offering a discount of lp for every second cup? Would the discount be compounded and would a third cup have cost only 69p? If the series continued arithmetically, then a fourth cup would cost 68p, the fifth 67p ... and the seventy- first cup would cost lp! And if I bought more than seventy- two cups, would they end up paying me money for every extra cup as the series went into negative values? In which case by the time I reached 143 cups, then the negative values would have cancelled out the earlier positive values and the bill would come to zero! And ordering a gross of cups of coffee would result in them paying me 72p to take them away! (... and perhaps now I see the derivation of the modern usage of 'gross').
These flights of fancy were curtailed and the mystery was solved when it was found that the till being used in the canteen calculated the bill exclusive of VAT and then added 17.5% to the total. One cup (excluding VAT) cost 60p, and then had 10.5p added in VAT, which is rounded up to a total of 71p. But two cups cost a1.20 (excluding VAT) which attracts a charge of 21p in VAT, making a total of a1.41, with no rounding required. Thus lp is saved if two cups are
bought together rather than separately. So it would appear that buying in bulk is rewarded by a reduction in the cost.
But in fact, it's not even that straightforward. The third cup would still have cost me another 71p (I'll leave you to do the calculation if you want). In order to save money, the strategy in this case would be always to buy cups of coffee in even numbers. So when going for coffee it's not a case of'the more the merrier', but rather 'two's company, three's a crowd'!
Generalizing further (with the assistance of a spreadsheet), there are some other possible anomalies which this till system might throw up.
For instance, if biscuits costs 9p each (exclusive of VAT), then one biscuit (inc VAT) would cost 1 lp, and two biscuits (inc VAT) would cost 21p - leading to a similar situation as for the coffee, where it is cheaper to buy in even numbers. Though in this case, the strategy breaks down when you get to eight people, with the eighth biscuit costing full price. So here, the strategy might be to go in groups of seven to get the best value!
However, if biscuits cost 8p (excluding VAT), then one biscuit (inc VAT) would cost 9p and two would cost 19p, making it cheaper to order your biscuits individually! So sometimes, being a loner isn't so bad after all ...
Author Tony Coles, Faculty of Education, UCE, Birmingham B42 2SU. e-mail: [email protected]
pizza
(nvlclolpzrzico One morning, I think I heard Chris Tarrant, on Radio 2, tell the nation that
The average American eats 18 acres ofpizza a year.
It seemed to me that this would make an interesting investigation which might capture the imagination of pupils and allow for a variety of approaches. The children of Sue Ingledew's (Y6) class at York Road School, Dartford, rose to
the challenge and some examples of their work are reproduced on the following pages. The Editors would be delighted to receive further samples of children's work on this statement.
Keywords: Investigation; Area.
Author LGJ
Mathematics in School, March 2003 The MA web site www.m-a.org.uk 19
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