Deceptively Difficult?

Question

Glass A is x% full of water, glass B is y% full of wine. If a tablespoon of water is taken from glass A and mixed with the wine in glass B, and then a tablespoon of the water-wine mixture in glass B is mixed with water in glass A, then in terms of x and y what percent of the water-wine mixture in glass A is water?

The glasses are the same size.

Answer 1

Underspecified - without knowing how large the glasses are, it is impossible to tell what fraction of the fluid in each glass one tablespoon is.

Answer 2

Good question, I can answer it with respect to 3 variables;

Let X be the total volume of water, Let Y be the total volume of wine, Let T be a scaler that when you multiply it with X or Y you get one tablespoon. This assumes that X and Y are the same volume.

So glass A at the start is just water ie A=X

then you remove one table spoon of it so A=X-TX
and B=Y+TX

you then remove one tablespoon from B so B becomes
B=Y+TX - T(Y+TX)
the table spoon of wine/water mix gets added to glass A again
A=X-TX +T(Y+TX) = T^2(X) + (Y-X)X +X

so the % of X in glass A = terms in X/terms in X and Y

therefore %X=[T^2(X) + -TX) + X]/[T^2(X) + (Y-X)X +X]

so you need to know how big the teaspoon is, and also assume that the volumes of wine and water are the same...

also come to think of it, how much water is in wine anyway? we need to know the %proof, or if its french wine or some cheap plonk... too many variables!!

:)

Answer 3

You didn't say how big each glass is related to tablespoons, so it is not possible to say.

Are you sure this is the question you want to ask? I have heard a similar one which asks "Is there more water in the wine or wine in the water?" The answer to this is deceptively easy - no need to calculate, there is the same amount in each, since the volumes did not change. (most people go down the path of computing how much water was moved, and how much was moved back.)

Answer 4

im guessing x/y%