and mix it thoroughly and take a tablespoon of that mixture and put it back into the pure coffee and mix that completely, is there more coffee in the creamer or more creamer in the coffee? (Please provide explanation or proof)
2006-09-15 07:25:19 · 5 answers · asked by ice_purple969 4 in Science & Mathematics ➔ Mathematics
x = volume of the tablespoon
y = volume of a cup
I calculate the amount of coffee in the creamer cup and the amount of creamer in the coffee cup:
Cup 1: (creamer)
Volume of creamer in the cup: y
Volume of coffee into the creamer: x
The fractions of the mixture are now: coffee x/(x+y) and creamer y/(x+y)
Volume of coffee taken out: x x/(x+y) or (x^2)/(x+y)
Volume of coffee remaining: x - (x^2)/(x+y) =
(x(x+y)-(x^2))/(x+y) =
(x^2 + xy - x^2)/(x+y) =
xy/(x+y)
Cup2: Coffee
Volume of creamer into the coffee is also xy/(x+y) since the fraction of creamer in cup 1 is y/(x+y)
=> it is the same
2006-09-15 08:11:58 · answer #1 · answered by mitch_online_nl 3 · 0⤊ 0⤋
You moved a tablespoonful of liquid from one cup to the other, and a tablespoonful of liquid back again. So at the end, there is the same total amount of liquid in each cup. But if there was more (or less) coffee in the creamer than creamer in the coffee, then one cup would have to be fuller (or emptier) than the other, and it isn't, so they're equal. No arithmetic, no algebra, just conservation of volume.
2006-09-15 16:42:12 · answer #2 · answered by bh8153 7 · 1⤊ 0⤋
There is more coffee in the creamer because when you add the tablespoon to the creamer, it is pure coffee but when you add the other tablespoon back, it is a mixture.
2006-09-15 14:41:35 · answer #3 · answered by MollyMAM 6 · 0⤊ 1⤋
cream is very light and has a lot of porosity so one tablespoon full of cream on mixing would probably become 1/2 or 3/4 spoon ful
have i answered your question?
2006-09-15 14:30:09 · answer #4 · answered by raj 7 · 0⤊ 1⤋
1 cup = 16 table spoon
Breaking this down step by step:
16 tbs cream ------------ 16 tbs coffee
16 tbs cream + 1 tbs coffee ------------- 15 tbs coffee
16*(16/17) tbs cream + 1*(16/17) tbs coffee ------------ 15 tbs coffee + (1/17 tbs coffee + 16/17 cream)
The cream cup ends up with 16/17 tbs of coffee in it, and the coffee cup ends up with 16/17 tbs cream in it. It's equal.
2006-09-15 14:31:12 · answer #5 · answered by lufen 3 · 0⤊ 0⤋