Question

a painter bought 8 gallons of paint just enough to cover 2 rooms. One room is twice the size of the other and requires only 2 coats Then the client decided not to paint the smaller room at all Let x be the # of gallons it takes for one coat of paint in the large room and the # of one coat of paint in the small room How many gallons will he have left

Answer 1

so, he's got 8 gallons of paint, to paint the two rooms, of the two rooms, one is twice as big as the other

now, "x" is how many gallons to paint the larger room with only one coat, however, the larger room uses 2 coats, so, the larger room uses 2x of paint
now, the client declined to paint the smaller one

so hmmm as I read... well, we dunno how many coats will go to the smaller room for one, we know the larger will use 2 coats, or 2x.. if we assume the smaller room was going to use say 1 coat or 1/2x

then one can say the painter bought enough for both rooms, 1coat for the small one and 2coats for the larger one

so, the paint the larger room, you'll 2x of paint, for 2coatsand to paint the smaller room, you'll need 1/2 x, because x gallons is how much is needed for the larger room, but the larger room is twice as big, thus the smaller room uses 1/2 of that in gallons

thus, with those assumptions, that the small room will use only 1 coat
$\bf \cfrac{1}{2}x+2x=8\implies \cfrac{5x}{2}=8\implies x=\cfrac{16}{5}$
that's who many gallons are needed for 1 coat in the larger roomrecall "x" is 1coat for the larger room

now, the client decides to skip the smaller roomso, the painter will only need 2x gallons then

$\bf 2x\implies 2\cdot \cfrac{16}{5}\implies \cfrac{32}{5}\implies 6.4\ gallons$

he bought 8 gallons, 8 - 6.4, he's got left 1.6 gallons