Problem: Parti-Gyle data for wort required from 3 kettles of same brew to produce 3 beers of different gravities

Knowns: Brew Lengths; Brew Gravities; Kettle Lengths; Kettle Gravities

Sample data: 1st brew - 50 barrels, 49.0 degrees; 2nd brew - 100 barrels, 41.0 degrees; 3rd brew - 200 barrels, 30.0 degrees; 1st kettle - 100 barrels, 78.0 degrees; 2nd kettle - 100 barrels, 41.0 degrees; 3rd kettle - 100 barrels, 8.0 degrees

Constraints: 1-100000 for length (whole numbers); 1.0-120.0 for gravity (decimals). All fields must be filled. Units are irrelevant providing consistent.