Sales of shovels have steadily declined at Als House of : PS Archive
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# Sales of shovels have steadily declined at Als House of

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03 Aug 2004, 13:01
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Sales of shovels have steadily declined at Alâ€™s House of Garden Implements; each day Alâ€™s sells one fewer shovel than it sold the previous day. Alâ€™s is open seven days a week, and sold 329 shovels during the first week in March. How many shovels will Alâ€™s sell during the second week in March if the trend continues?
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03 Aug 2004, 14:24
Also an excellent question. Very cool.

280.

(I'm not posting how I did it so everyone can try)
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03 Aug 2004, 19:13
let X be the no. of shovels sold the first day in March. We then have

X + (X-1) + (X-2) + (X-3) + (X-4) + (X-5) + (X-6) =329

or X = 50. So the seventh day, he has sold 50-6 = 44 shovels.

Now in the following week Al would have sold

43+42+41+40+39+38+37 = 280.
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03 Aug 2004, 20:41
280. used arithmetic progression to get that.
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03 Aug 2004, 21:45
2 monday would have been 7 less than first monday,
2 tuesday would have been 7 less than first tuesday,
and so on (repeats seven times for each day of the week).

Sales at second week = sales at first week - 7*7 = 329 - 49 = 280
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04 Aug 2004, 11:30
Right again gang. OA is 280.
04 Aug 2004, 11:30
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# Sales of shovels have steadily declined at Als House of

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