Final answer:
To find the width of the rug, we convert the area and length to improper fractions and divide the area by the length. The width is found to be 2 3/4 yards.
Step-by-step explanation:
The student is asking for the width of a rectangular rug given its area and length. To find the width, we will use the formula for the area of a rectangle, which is Area = Length × Width. First, we must convert the mixed numbers to improper fractions for easier calculations. The area is given as 15 7/12 square yards, which is (15 × 12 + 7) / 12 = 187/12 square yards. The length is given as 5 2/3 yards, which is (5 × 3 + 2) / 3 = 17/3 yards. To find the width, we divide the area by the length:
Width = Area / Length = (187/12) / (17/3) = (187/12) × (3/17) = 187/12 × 3/17 = 11/4 = 2 3/4 yards.
Thus, the width of the rug is 2 3/4 yards.