the auroran sunset ([info]tithonus) wrote,
@ 2003-11-22 07:07:00
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Current mood: amused
Current music:D:Ream - Things Can Only Get Better

the difference between a mathematician and a numerate
an amusing example of the difference between someone who can do maths, and someone who is nummerate!... [info]micina asked her readers how to solve the following..

A group of old ladies meet for an afternoon tea party. They bring all their cats. In all, there are 22 heads and 72 feet. How many old ladies and how many cats are in the room?

a) 6 old ladies and 16 cats
b) 7 old ladies and 15 cats
c) 8 old ladies and 14 cats
d) 9 old ladies and 13 cats
e) 10 old ladies and 12 cats

by the time i saw it this morning, someone had already explained how to solve this using simultaneous equations. admittedly i did vaguely considering doing that when i first saw it, but not for long.. here's my response:

alternatively, as you have the answers it may be quicker just to work out which fits..
eg. a) head: 6+16=22 (ok) feet: (6*2)+(16*4)=76 (wrong)
as they all subsusquent answers just add one human and subtract one cat, the number of heads doesn't change, and the number of feet goes down my two each time [-cat feet+human feet]. you need to subtract 4 from the feet, so the answer must be (c).

you may find that an easier method and much quicker!.. simultaneous equations are useful, but not always necessary. :-)

not often that i get examples of differences in response between a mathematician and a nummerate.. the mathematician [unless nummerate of course] will tend to do it the formula way every time no matter how long it takes, and is highly unlikely to see lower tech shortcuts.. for someone else's comments on this sort of thing see here.

update: it occured to me in the shower that my method is better even if there are no answers... make a stupid guess like 1 granny and 21 cats [idea making the heads right].. work out that this makes 86 feet. realise that this 14 too many. realise that this means swapping 7 cats into grannies.. voila: 8 grannies and 14 cats. still much quicker and easier than simultaneous equations. &=&


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[info]irisetta
2003-11-22 03:00 am UTC (link)
Yes, that is slightly kinder on my poor brain ;) tbh, I still can't quite work out the reasoning of that simultaneous equation Ben showed me... plus I'm always inclined to just make silly guesses with that sort of thing... my brain works in random ways it wouls seem :) I thought you did your degree in a maths-type subject?

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[info]tithonus
2003-11-22 04:01 am UTC (link)
what part of the simultaneous equations stuff is unclear? i'll happily try to put it into english if you wish. ~_~ [a possible suggestion: try working through the reasoning with piles of coins of two types - always relate it back to something *real*].

and yes i did do a maths type degree, and i spent a lot of the time boggling at the accolytes with their silly holy texts and lack of real world sense. the way maths is usually taught really bugs me: that so many people grow up to think that there is something intrinsically difficult about something so simple and useful, and at the same time those that are "good" at it largely have no clue how to relate it reality, is a sure sign of unbelievable incompetence... maths is just another language [an incredibly simplified one at that], so a linguist like yourself *should* be in their element...

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[info]irisetta
2003-11-22 07:07 am UTC (link)
If you could help me out that'd be great...

o is no. old ladies, c is no. cats.

we know
o + c = 22
2o + 4c = 72

so
2o + 2c = 44

subtract one from the other
(2o - 2o) + (4c - 2c) = (72 - 44)
2c = 28
c = 14

o + c = 22
o = 22 - c
o = 22 - 14
o = 8

so 8 ladies and 14 cats

I honestly need talking through the whole thing step-by-step like a baby :( The harder I squint at the whole process the less it makes sense... It's ridiculous because I remember being able to do this sort of thing at school, though admittedly equations were never my strong point. You're right about the maths/languages analogy; I did one of those Morrisey aptitude tests when I was about 16 and my numerical reasoning score was only a little under my verbal ability... I blame my present crapness on shit teaching and the fact that they refused to put me up a set in Maths before my GCSEs! *g*

Thanks hon! :)





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