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A painter bought 10 gallons of paint, just enough to cover two rooms. One room is twice the size of the other and requires three coats of paint. The smaller room requires only two coats. 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?
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x + y = 8
x = 2y
2y + y = 8
3y = 8
y = 8/3 = 2 2/3
x = 2y
x = 2(8/3)
x = 16/3 = 5 1/3
x + y = 8
8/3 + 16/3 = 8
24/3 = 8
8 = 8 (correct)
large room uses 5 1/3 gallons
smaller room uses 2 2/3 gallons
However, the smaller room was not painted, therefore, 2 2/3 gallons were left over.