Essentials Ch2 review question!!

[noname]

Hey guys, just need some help on the following question:



Having some trouble here :/

Any help would be much appreciated,
Barry

[pi]

I remember spending hours on this question back in yr11, its a bitch. Not even my GMA teacher could do it, although we DID end up solving it with the help of two other teachers. I have no idea how to do it now, but if I can find the solution, I'll post it up.

[noname]

I remember spending hours on this question back in yr11, its a bitch. Not even my GMA teacher could do it, although we DID end up solving it with the help of two other teachers. I have no idea how to do it now, but if I can find the solution, I'll post it up.

Haha, all right then. Thanks

[Will T]

The ratio of wine to water for Bottle A is 2:1. The ratio of wine to water for Bottle B is 1:5.

This is the same as 2/3 wine and 1/3 water in Bottle A and 1/6 wine and 5/6  water in Bottle B.

Let k denote the amount of water taken out of Bottle A. Let j denote the amount of water taken out of Bottle B. As the capacity of the third bottle is 1, this means k + j = 1.
If you take k litres out of A, you end up with 2k/3 litres of wine and 1k/3 litres of water. Therefore you must take 1-k litres out of B. This results in (1-k)/6 litres of wine and 5/6(1-k) litres of water.

When you add the litres of water together, it must equal the litres of wine.

Therefore: 2k/3 + (1-k)/6 = k/3 + 5(1-k)/6
4k/6 + (1-k)/6 = 2k/6 + 5(1-k)/6
4k+1-k = 2k + 5 - 5k
6k = 4
Hence, k = 2/3.
Therefore, you take 2/3 litres out of Bottle A and 1/3 Litres out of Bottle B.

Following this logic you can work out the next parts. But I can also supply solutions for b) and c) if you would like.