Apainter bought 8 gallons of paint, just enough to cover two rooms. one room is twice the size of the other and requires 3 coats of paint. the smaller room requires only 2 coats. then the client decided not to paint the smaller room at all. how many gallons of paint are left

Let x be the size of the small room and 2x, the big room

The larger room requires 3 coats and the smaller, 2 coats

All requires exactly 8 gal.

2.x + (2x).3 = 8 Gal,  8x = 8 and x = 1 (size of te smallest)

if it's the small room, then it will need 2 coats or 2x1 = 2 Gal,  and the paint left is 8-2  = 6 Gal.

if it's the large one, 6x or 6 Gal, and remaining 2 Gal

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