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        riddles >> easy >> Buy Banana
        
(Message started by: R on Mar 16^th, 2010, 9:40am)

Title: Buy Banana
Post by R on Mar 16^th, 2010, 9:40am

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?

Title: Re: Buy Banana
Post by towr on Mar 16^th, 2010, 10:02am

[hide]#red = 3/4*#yellow + 12[/hide]

Title: Re: Buy Banana
Post by R on Mar 16^th, 2010, 10:10am

Got a similar result, but after manipulating two equations. Just curious, how did you deduce it?

Title: Re: Buy Banana
Post by towr on Mar 16^th, 2010, 10:25am

[hide]
[(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
[/hide]

Title: Re: Buy Banana
Post by R on Mar 16^th, 2010, 10:31am

I solved it slightly differently. Using the equation:

3y + 4r = 24k for some positive integer k.

Title: Re: Buy Banana
Post by Grimbal on Mar 17^th, 2010, 3:10am

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.

Title: Re: Buy Banana
Post by towr on Mar 17^th, 2010, 3:35am

Ah, I forgot to use the fact that we have the same number of red and yellow bananas at the start.
[hide]
#red = 3/4*#yellow + 12
#red = #yellow
=>
#red = #yellow = 48
[/hide]

Title: Re: Buy Banana
Post by ThudanBlunder on Mar 17^th, 2010, 6:26am

[hide]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[/hide]

Here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1232876435;) is a similar puzzle.

Title: Re: Buy Banana
Post by tenchi on Mar 17^th, 2010, 8:37am

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.

Title: Re: Buy Banana
Post by R on Mar 17^th, 2010, 9:07am

on 03/17/10 at 03:35:29, towr wrote:

Ah, I forgot to use the fact that we have the same number of red and yellow bananas at the start.

Ahhh!! me too... ;D ;D ;D

Title: Re: Buy Banana
Post by ephyzy on Mar 23^rd, 2010, 10:33pm

Quote:

Ok, this is my first day here and if this is the easy section I am in trouble!

LOL I have the exact same thoughts right here! :D ;D