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Topic: Buy Banana (Read 906 times) |
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R
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How it is that when I buy yellow bananas at three shillings a bunch and the same number of red ones at four shillings a bunch I would get two more bunches for the same amount if I divided the money evenly between the yellow and red bananas?
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R
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Re: Buy Banana
« Reply #2 on: Mar 16th, 2010, 10:10am » |
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Got a similar result, but after manipulating two equations. Just curious, how did you deduce it?
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towr
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Re: Buy Banana
« Reply #3 on: Mar 16th, 2010, 10:25am » |
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[(y*3+r*4)/2]/3 + [(y*3+r*4)/2]/4 = y+r + 2
y*3/6+r*4/6 + y*3/8+r*4/8 = y+r + 2
y*4/8+r*4/6 + y*3/8+r*3/6 = y+r + 2
y*7/8+r*7/6 = y+r + 2
r/6 = y/8 + 2
r = 3/4*y + 12
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R
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Re: Buy Banana
« Reply #4 on: Mar 16th, 2010, 10:31am » |
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I solved it slightly differently. Using the equation:
3y + 4r = 24k for some positive integer k.
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Grimbal
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Re: Buy Banana
« Reply #5 on: Mar 17th, 2010, 3:10am » |
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Funny, I have no idea what you are talking about.
Isn't the question to find the amount available?
If I start with an amount of 3*4*7*2=168 (conveniently a multiple of 3, 4, 3+4, plus a factor 2 for "divide the money equally"), I find
- same number of Y and R: 3*4*2 = 24 of each, 48 altogether
- same amount: 4*7 = 28 R and 3*7 = 21 Y, 49 altogether
Since the difference is 1 bunch, the available amount is twice what I started with, i.e. 336 shillings.
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| « Last Edit: Mar 17th, 2010, 10:26am by Grimbal » |
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towr
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Re: Buy Banana
« Reply #6 on: Mar 17th, 2010, 3:35am » |
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Ah, I forgot to use the fact that we have the same number of red and yellow bananas at the start.
#red = 3/4*#yellow + 12
#red = #yellow
=>
#red = #yellow = 48
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ThudnBlunder
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Re: Buy Banana
« Reply #7 on: Mar 17th, 2010, 6:26am » |
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Firstly, let x bunches of both yellow and red bananas be bought.
Then total cost = 7x shillings.
Now 7x/2 is spent on both yellow and red.
This can buy 7x/6 bunches of yellow and 7x/8 bunches of red.
Total = 49x/24 bunches.
It is given that this equals 2x + 2 bunches.
Hence x = 48 and cost = 336 shillings.
Second time around, 56 yellow and 42 red are bought.
More generally, if the yellow and red bananas cost respectively y and r shillings per bunch and spending the money equally enables k more bunches to be bought
then
x = 2yrk/(y - r)2
and
Cost = 2yrk(y + r)/(y - r)2
Here is a similar puzzle.
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| « Last Edit: Mar 19th, 2010, 3:13am by ThudnBlunder » |
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tenchi
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Re: Buy Banana
« Reply #8 on: Mar 17th, 2010, 8:37am » |
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Ok, this is my first day here and if this is the easy section I am in trouble! I am 46 and back in school so I need to brush up a bit. It is good to see the answers though so I can work through the problem/riddle myself.
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R
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Re: Buy Banana
« Reply #9 on: Mar 17th, 2010, 9:07am » |
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on Mar 17th, 2010, 3:35am, towr wrote:Ah, I forgot to use the fact that we have the same number of red and yellow bananas at the start.
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Ahhh!! me too... 
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ephyzy
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Re: Buy Banana
« Reply #10 on: Mar 23rd, 2010, 10:33pm » |
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Quote:
Ok, this is my first day here and if this is the easy section I am in trouble!
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LOL I have the exact same thoughts right here! 
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