Winnie likes her lemonade to have a water:lemon juice ratio of 7:2. Lizzie prefers a water: lemon juice ratio of 6:1. How much water would Lizzie have to add to 450 gallons of Winnie's lemonade in order for it to be to her liking?
Winnie's lemonade: 450 gallons of a 7 water : 2 lemon juice ratio
Add the 7 parts of water to the 2 parts of lemon juice to get a total of 9 parts.
Therefore the 450 gallons have (2/9)·450 gallons = 100 gallons of lemon juice
and (7/9)·450 gallons = 350 gallons of water.
Lizzie needs to have 600 gallons of water for every 100 gallons of lemon juice.
There are already 350 gallons of water; she will need to add another 600 - 350 = 250 gallons of water.