1 inch = 1/12 foot
27 cubic feet = 1 cubic yard
Volume = 1,500 x 1/12 = 125 cubic feet = 417/27 cubic yards (rounded, that's 4.63)
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1500 sq ft * 4 inches = 1500/9 sq yards * 1/9 yards = 18.518518... cubic yards.
You need 166.66 square yards of carpet.
There are 3 square feet in a square yard, so divide 4500 by 3.4500/3=1500 square yards
166 and 2/3
46.87