ratio of parts

Thanks Chris, 

I like this question and your answer.

I do rations in rather weird ways.  For basic quesions my way is REALLY easy.

BUT for harder questions I often get in a mess.

This is how I tacked this one.

So the ratio of orange juice to lemonade is    6/7   :   4      = 6:28  =      3:14

For every 7  gallons of water in the original mixture, the orange juice concentrate comprises 2 gallons.

So, if this 7 gallons  is mixed with lemonade in a ratio of 3 : 4....there must be  7 x (4/3)  = 28/3  gallons of

lemonade in this mixture.

Then the ratio of orange juice concentrate to lemonade in this mixture is   2  : 28/3    =  6 : 28 =  3 : 14