The Deflating Mangoes

quote:

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The Lotaseetas have a rather casual attitude to commerce. Every Monday morning, Ming, the rice-planter, gathers from the grove outside his bungalow a number of mangoes of uniform weight. For the rest of the week he uses these as weights for measuring out the rice on his scales, charging each customer according to the number of mangoes required to balance the weight purchased.

Unfortunately, the mangoes themselves lose a fixed percentage of their weight each day by evaporation. However, Ming roughly compensates for this by using two mangoes as the unit on Wednesdays and Thursdays and three mangoes on Fridays. Clearly, Wednesday is a good day for buying rice and Tuesday is a bad day.

His first customer at precisely 10 o'clock each morning (they are late risers) is Fung, the rice merchant, who always buys the same quantity of rice for his shop. On Monday Fung's rice cost him 243 cowries. On Friday it cost him 256 cowries.

How much did it cost him on Tuesday?

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I gave the math a try, but I am still stuck with two variables and one equation. Will give it another try a little later.

I played with the math and got 164.167 or 164 1/6. Close at all?

the answer is a whole number
curiously, it's around twice the value of what you've posted

Okay, I had a plus sign that should have been a minus sign.

Is it 322 cowries?

warmer!

the answer's in the 320s

that's a gimme

the answer is 324

Could you perhaps explain the answer?? Have been thinking about this one for quite some time, but no way I could solve it...

hope you can read this, as keyboards and formulae aren't that friendly

taking the weight of one mango on Monday as W units, on Tuesday as We, on Wednesday as We2, on Thursday We3 and on Friday as We4, then the cost of the quantity of rice R is:

[ e is less than one as the weight of the mangoes falls each day by evaporation, and is a constant ]
[ 2 means squared, 3 mean cubed etc. ]

Monday: R/W currency units [ 243 ]
Tuesday: R/We currency units
Wednesday: R/2We2 currency units
Thursday: R/2We3 currency units
Friday: R/3We4 currrency units [ 256 ]

thus: Monday/Friday = (R/w)/(r/3We4) = 3e4 = 243/256
and further elimination of 'common factors' gives: e4=81/256
which itself gives: e=3/4
[ e equals three-quarters ]

and therefore Tuesday's cost: (Monday's cost)/e = 243/(3/4) = 324

the daily costs were:
Monday 243
Tuesday 324
Wednesday 216
Thursday 288
Friday 256

anyone know how to write e squared on a keyboard?
e2

[ June 08, 2002, 08:41 PM: Message edited by: gtho4 ]

Thanks George! I could read it perfectly well, even with the missing superscripts! I have no clue how to make them. Copying from Word doesn't work...