Wild potatoes
#888015
05/16/13 12:41 PM
05/16/13 12:41 PM
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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
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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.
I'm a man of few words, BUT I use 'em often!!
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Re: Wild potatoes
[Re: CanukDenis]
#888152
05/17/13 03:39 AM
05/17/13 03:39 AM
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Joined: Mar 2004
Posts: 11,846 Isle of Man
Lex
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Isle of Man
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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?
Last edited by Lex; 05/17/13 03:42 AM.
Life is what happens while you're making other plans.
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Re: Wild potatoes
[Re: CanukDenis]
#888347
05/18/13 02:49 AM
05/18/13 02:49 AM
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Joined: Mar 2004
Posts: 11,846 Isle of Man
Lex
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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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Re: Wild potatoes
[Re: Lex]
#888425
05/18/13 11:07 AM
05/18/13 11:07 AM
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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
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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 'em often!!
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Re: Wild potatoes
[Re: CanukDenis]
#888504
05/18/13 09:01 PM
05/18/13 09:01 PM
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Joined: Jan 2003
Posts: 5,763 Mojave desert, California
CCbomber
BAAG Specialist
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BAAG Specialist
Joined: Jan 2003
Posts: 5,763
Mojave desert, California
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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
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Re: Wild potatoes
[Re: CanukDenis]
#888539
05/19/13 12:32 AM
05/19/13 12:32 AM
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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
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Ottawa Ontario Canada
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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.
I'm a man of few words, BUT I use 'em often!!
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