Apainter bought 16 gallons of paint, just to cover two rooms. one room is twice the size of the other room and requires three coats of paint the smaller room requires only two coats of paint. then the client decided not to paint the smaller room after all. let x be the number of gallons it takes for one coat of paint in the large room and y the number for one coat of paint in the small room. how many gallons of paint will be left?

The total number of gallons of paint needed for the big room is 3x and the number of gallons of paint needed for the small room is 2y. 
                                   3x + 2y = 16
Given the sizes of the room, the relation should be that,
                                    x = 2y
Solving the equation,
                                      3(2y) + 2y = 16
                                               y = 2
Therefore x is equal to 4 gallons. 
With the condition that only the bigger room is painted, the number of gallons of paint used should be 12 gallons and what is left should be 4 gallons.