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#888015 - 05/16/13 12:41 PM Wild potatoes
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 15103
Loc: Ottawa Ontario Canada
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.
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#888023 - 05/16/13 01:14 PM Re: Wild potatoes [Re: CanukDenis]
bermag45 Offline
BAAG Specialist

Registered: 10/31/03
Posts: 5067
Loc: Deepest darkest Norfolk, Engla...
In order for me to work this out I really do need to know the exact location of "some forest". Thank you Denis! thumbsup wave

Bernie happydance

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#888026 - 05/16/13 01:25 PM Re: Wild potatoes [Re: CanukDenis]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 15103
Loc: Ottawa Ontario Canada
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 wink
_________________________
I'm a man of few words...but I use them often

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#888070 - 05/16/13 04:22 PM Re: Wild potatoes [Re: CanukDenis]
Lex Offline
Addicted Boomer

Registered: 03/07/04
Posts: 4845
Loc: Isle of Man
I usually employ staff to do stuff like picking potatoes... wink
_________________________
Life is what happens while you're making other plans.


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#888078 - 05/16/13 05:17 PM Re: Wild potatoes [Re: Lex]
bermag45 Offline
BAAG Specialist

Registered: 10/31/03
Posts: 5067
Loc: Deepest darkest Norfolk, Engla...
Sorry Denis, I only do apples in Sherwood Forest, not potatoes pal! wave thumbsup

Bernie happydance

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#888152 - 05/17/13 03:39 AM Re: Wild potatoes [Re: CanukDenis]
Lex Offline
Addicted Boomer

Registered: 03/07/04
Posts: 4845
Loc: Isle of Man
I think this would probably have been a Borris family outing in a Canadian forest with all that thieving sibling rivalry going on. lol

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


Edited by Lex (05/17/13 03:42 AM)
_________________________
Life is what happens while you're making other plans.


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#888347 - 05/18/13 02:49 AM Re: Wild potatoes [Re: CanukDenis]
Lex Offline
Addicted Boomer

Registered: 03/07/04
Posts: 4845
Loc: Isle of Man
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...!
_________________________
Life is what happens while you're making other plans.


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#888425 - 05/18/13 11:07 AM Re: Wild potatoes [Re: Lex]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 15103
Loc: Ottawa Ontario Canada
Originally Posted By: Lex
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


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?


_________________________
I'm a man of few words...but I use them often

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#888481 - 05/18/13 06:03 PM Re: Wild potatoes [Re: CanukDenis]
bermag45 Offline
BAAG Specialist

Registered: 10/31/03
Posts: 5067
Loc: Deepest darkest Norfolk, Engla...
Suitably chastised Denis lol wave

Bernie happydance

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#888504 - 05/18/13 09:01 PM Re: Wild potatoes [Re: CanukDenis]
CCbomber Offline
Addicted Boomer

Registered: 01/16/03
Posts: 3148
Loc: Mojave desert, California
a = # potatoes Art picked = 1
b = # potatoes Ben picked = 200
c = # potatoes Cam picked = 4
grin happydance

The bloody details, sleep

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

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#888539 - 05/19/13 12:32 AM Re: Wild potatoes [Re: CanukDenis]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 15103
Loc: Ottawa Ontario Canada
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.
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I'm a man of few words...but I use them often

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