Art, Ben and Cam rented a cabin in some forest.
All 3 left early one morning each with a potato
sack, and went looking for wild potatoes.

They got back to the cabin during the evening,
placed their sacks against a kitchen wall, and,
tired, all went to bed for the sleep of the unjust.

During the evening, the following events took place:
1: Art got up, tiptoed to the kitchen, took 1/5
of the potatoes in Ben's sack and 1/4 of the
potatoes in Cam's sack, put 'em in his sack, then
went back to bed.
2: later, Ben got up, tiptoed to the kitchen, took
1/3 of the potatoes left in Art's sack and 1/3 of
the potatoes left in Cam's sack, put 'em in his
sack, then went back to bed.
3: later, Cam got up, tiptoed to the kitchen, took
1/7 of the potatoes left in Art's sack and 1/5 of
the potatoes left in Ben's sack, put 'em in his
sack, then went back to bed.

After a careful investigation, following was discovered:
1: total wild potatoes originally picked = 205
2: Art ended up with 6 times the potatoes that Cam originally picked
3: Ben ended up with 60 fewer potatoes than he originally picked

Your mission: figure out how many each guy picked.

In order for me to work this out I really do need to know the exact location of "some forest". Thank you Denis!

Bernie

How about Sherwood Forest, Bernie; close enough to
you out there in Norfolk?

http://www.google.ca/search?q=map+sherwo...024&bih=662

And, if you wish, I can change the pickers to Bernie, Lex and Rog

I usually employ staff to do stuff like picking potatoes...

Sorry Denis, I only do apples in Sherwood Forest, not potatoes pal!

Bernie

I think this would probably have been a Borris family outing in a Canadian forest with all that thieving sibling rivalry going on.

Isn't there a puzzle to solve in this thread somewhere?

According to my somewhat rusty and inadequate maths, the equations needed must look something like this, where a, b and c are respectively the numbers of potatoes picked by Art, Ben and Cam:

a + b + c = 205

6{(a + b/5 + c/4) - (a/3 + 4b/5 + c/4)}/7 = 6c

3b/5 + 4(a/3 + c/3)/5 = b - 60

Trying to work the answer out may well be beyond me...!

1st equation is correct !!

2nd you don't really need (not correct anyway!)

3rd you do need, but left side is incorrect.
When Ben takes from Art and Cam, he is not
taking a/3 and c/3, but is taking 1/3 of what
was left after Art did his tiptoeing!

Say we start with: a=50, b=60, c=40
Then Art took 12 from Ben and 10 from Cam,
leaving Ben with 48, Cam with 30, himself with 72.
So when Ben goes tiptoeing, he will take 1/3
of 72 and 1/3 of 30.

Ya'll ok now?

Suitably chastised Denis

Bernie

a = # potatoes Art picked = 1
b = # potatoes Ben picked = 200
c = # potatoes Cam picked = 4


The bloody details,

After Art tiptoes,
Art's sack contains a + b/5 + c/4
Ben's sack contains 4b/5
Cam's sack contains 3c/4

After Ben tiptoes,
Art's sack contains,
(2/3)(a + b/5 + c/4)
= 2a/3 + 2b/15 + c/6
Ben's sack contains,
4b/5 + [(1/3)(a + b/5 +c/4)] + (1/3)(3c/4)
= a/3 +13b/15 + c/3
Cam's sack contains,
(2/3)(3c/4)
= c/2

After Cam tiptoes,
Art's sack contains,
(6/7)(2a/3 + 2b/15 + c/6)
= 12a/21 + 12b/105 + c/7
= 4a/7 + 4b/35 + c/7
Ben's sack contains,
(4/5)(a/3 + 13b/15 + c/3)
= 4a/15 + 52b/75 + 4c/15
Cam's sack contains, (but is not needed)
c/2 + (1/7)(2a/3 + 2b/15 + c/6) + (1/5)(a/3 + 13b/15 + c/3)
= 2a/21 + a/15 + 2b/105 + 13b/75 + c/2 + c/42 + c/15

We're given,
1. a+b+c = 205
2, 4a/7 + 4b/35 + c/7 = 6c
3. 4a/15 + 52b/75 + 4c/15 = b-60

From 3,
(20a+52b+20c)/75 = b-60
20a+52b+20c = 75b-4500
20a+20c = 23b -4500
20(a+c) = 20(205-b) = 23b-4500
4100-20b = 23b -4500
43b = 8600
b =200 (and we now know a+c =5)

From 2,
(20a+4b+5c)/35 = 6c
20a+4b+5c = 210c
20(5-c)+800 = 205c
100-20c+800 = 205c
900 = 225c
c=4 and a=1

Correct. Can be shortened:

"(20a+52b+20c)/75 = b-60
20a+52b+20c = 75b-4500
20a+20c = 23b -4500
20(a+c) = 20(205-b) = 23b-4500
4100-20b = 23b -4500
43b = 8600
b =200 (and we now know a+c =5)"

At this point, we know c has to equal 4,
since Art took 1/4.