The three apple farmers (Mike, Juliet, and Bob) finished their harvest and reported yields of 314,827 apples, 1,199,533 apples, and 683,786 apples, respectively. Mike mentioned the number of apples he'd have left over if he divided his harvest equally among all the apple dealers in the area. Juliet indicated she would have bought the extra apples so she could divide her supply equally among the dealers, with Bob indicating the same thing. How many apple dealers are there?

Probably less than the number of meth dealers...

There are 9,157 dealers.

Thanks, X.

Now I'm going to be thinking about this for the rest of the day

131

If he divided his apples equally among all the dealers, he would have just a few or even zero apples left over. It cannot be determined how many dealers there are from this scenario.

Or if it can, I don't have the time to do it!

^

ed zachary....as long as there are apples at my dealer, WGAF. 🙂

As of November 2009, Apple has opened 280 stores; 219 in 41 US states, 24 in the United Kingdom (20 in England, two in Scotland, one in Northern Ireland and one in Wales), 14 in Canada, 7 in Japan, 6 in Australia, 3 in Switzerland, 2 each in Germany, Italy and France and 1 in China.[1]

Of course this does not include 3rd party retailers.

Apples don't grow on trees, ya know...

It seems to be a pretty simple math question...

If # of dealers = x

And the remainder of mikes harvests = Rm

Then

(1199533 + Rm)/X = whole number (Nj)

(683786 + Rm)/X = whole number (Nb)

(314827 - Rm)/X = whole number (Nm)

One could figure it out with brute force...

but it seems that we should be able to relate them in another manner...

X = (314827 - Rm)/Nm

--> [(683786 + Rm)/(314827 - Rm)]*Nm=Nb

Probably could figure something out from that....

Or just put it in a spread sheet. I just set up some formulas and came up with 131. If you take 314,827/131, that equals 2403.26 apples per dealer. Round that down to 2403. Take that times the 131 dealers and you have 314,793 going to the dealers, that leaves 34 apples left over. Add that to the other two totals and divide them by 131 and those come out even so that means no apples would have remained.

Where'd you get the 131?

Wrote formulas using 1 dealer, then 2 dealers on the next line and so on. Drag the formulas down, find the one that has them coming out as whole numbers.

Wonderful, the great "Apple Dealers" mystery of fall 2009 has been solved!

lol... 131 is the common answer so far.. a friend of mine found 9 somehow. I've been trying to figure how he came up with it....

Speaking of apples, I could go for a good Dickins Cider...

When she's really parched, say "open wider." She's gonna want a big Dickins Cider.

another solution-

314827/7 = 44975 plus 2 left over.

1199553 + 2 = 1199555, / 7 = 171365

683786 + 2 = 683788, / 7 = 97684

Seven is the smallest number that can be divided evenly..

there is only one. the others work for him.

wow... one would work..