Comments on: [WCYDWT] Coke v. Sprite

By: mr bombastic

mr bombastic — Sun, 12 Aug 2012 13:22:01 +0000

James Tanton has this problem along with some variations:

By: AstridWang

AstridWang — Thu, 24 May 2012 23:01:36 +0000

assume* sorry

By: AstridWang

AstridWang — Thu, 24 May 2012 23:01:09 +0000

THE SAME

Assue Y is how much original liquid you have for each cup (which is both Y)

X is how much liquid you take out each time (and in this case you take out the same amount of liquid in two transfer).

how much original liquid in sprite: Y-X+X(X/X+Y), which =Y^2/X+Y

how much original liquid in:Y-X(Y/X+Y), which =Y^2/X+Y

if you simplify your expressions nicely LOL

am a 9th grader, my teacher showed us this today and she told us she didn’t no how to do this, WHAT?!

I think this is the easiest way to do this, I did it with simple number too(you should’ve have ratio thing comes in!), think this is more convincing and abstract, and more like Mathematics

Be friends w/me ppl :p

By: zaq

zaq — Fri, 09 Mar 2012 16:59:15 +0000

sprite for sure

By: Erin

Erin — Sun, 22 Jan 2012 15:40:26 +0000

Kids (7&9) figured this out using legos and then starbursts. Their first instinct was that the “coke” side would end up with more, then they tried to figure it our using simpler numbers and my son changed his mind to “same”. We wanted him to prove it but the numbers were more difficult to use for him so he grabbed 20 of each of two colors of legos and demonstrated his thinking. Then, for fun, did it with starbursts too. Each time they worked it out with the manipulatives it ended up the same. My daughter (7) needed to see it over and over again to believe it but was finally convinced. Great way to spend a Sunday morning!!

By: Alexis Piazza

Alexis Piazza — Fri, 25 Nov 2011 04:56:01 +0000

Leave it to my sister to develop an elegant, visual way to solve this problem. Using the smallest units

The link is here: http://mrpiazzamath.tumblr.com/

Frame 1 – Two equals parts of Sprite and Coke

Frame 2 – Move 1 part of Sprite to Coke, which is now 2 parts Coke and 1 part Sprite.

Frame 3 – The mixture dissolves. 1/3 of each unit is now Sprite, 2/3 is now coke.

Frame 4 – Move 1 unit of SpriteCoke (1/3 Sprite, 2/3 Coke) to Sprite. You can see there are 4/3 Sprite on the left and 4/3 Coke on the right.

By: GM from MooseJaw

GM from MooseJaw — Mon, 31 Oct 2011 21:34:52 +0000

slight edit to above:

x is any fractional value less than 1 greater than 0

(my use of the less than and greater than sign in my post removed the contents between…)

By: GM from MooseJaw

GM from MooseJaw — Mon, 31 Oct 2011 21:31:23 +0000

Generalizing:
x is any fractional value 0
Coke side after addition of fraction of S:
C+xS
Coke side after removal of same volume just added:
C+xS — x/(1+x) (C+xS)
Sprite side after adding back above removal:
S-xS + x/(1+x) (C+xS)
Multiply both formulae by (1+x):
(1+x)C+(x+xx)S -x(C+xS) = C+xC+xS+xxS-xC-xxS
(1+x)S-(x+xx)S +x(C+xS) = S+xS-xS-xxS+xC+xxS
Simplify and divide by 1.1
(1C+xS)/(1+x)
(1S+xC)/(1+x)

By: GM

GM — Mon, 31 Oct 2011 21:02:19 +0000

Coke side after addition of fraction of S:
C+0.1S
Coke side after removal of same volume just added:
C+0.1S – 0.1/1.1 (C+0.1S)
Sprite side after adding back above removal:
S-0.1S + 0.1/1.1 (C+0.1S)
Multiply both formulae by 1.1:
1.1C+0.11S -0.1 (C+0.1S) = 1.1C-0.1C +0.11S-0.01S
1.1S-0.11S +0.1(C+0.1S) = 1.1S-0.11S+0.01S+0.1C
Simplify and divide by 1.1
(1C+0.1S)/1.1
(1S+0.1C)/1.1

By: Dan Meyer

Dan Meyer — Tue, 18 Oct 2011 20:54:08 +0000

Awesome. What were the demographics on the class?