To solve this problem, we need to determine the cost of carpeting a room with the given dimensions and cost per unit area. Let's break this down step-by-step:
1. Convert the room dimensions from fractions to decimal feet:
- Length: [tex]\(16 \frac{1}{2}\)[/tex] feet can be written as [tex]\(16.5\)[/tex] feet.
- Width: [tex]\(18 \frac{1}{2}\)[/tex] feet can be written as [tex]\(18.5\)[/tex] feet.
2. Convert the dimensions from feet to yards:
- Since [tex]\(1\)[/tex] yard equals [tex]\(3\)[/tex] feet, we need to divide the dimensions in feet by [tex]\(3\)[/tex].
- Length in yards: [tex]\( \frac{16.5 \text{ feet}}{3} = 5.5 \text{ yards} \)[/tex]
- Width in yards: [tex]\( \frac{18.5 \text{ feet}}{3} = 6.16666666667 \text{ yards} \approx 6.17 \text{ yards} \)[/tex]
3. Calculate the area of the room in square yards:
- Area = Length [tex]\(\times\)[/tex] Width
- Area = [tex]\( 5.5 \text{ yards} \times 6.16666666667 \text{ yards} = 33.91666666667 \text{ square yards} \approx 33.92 \text{ square yards} \)[/tex]
4. Calculate the total cost of carpeting the room:
- The cost per square yard is [tex]\( \$17.50 \)[/tex].
- Total cost = Area [tex]\(\times\)[/tex] Cost per square yard
- Total cost = [tex]\( 33.91666666667 \text{ square yards} \times \$17.50 \text{ per square yard} = \$593.54166666667 \approx \$593.54 \)[/tex]
5. Round the total cost to the nearest dollar:
- Rounded total cost = [tex]\( \$594 \)[/tex]
Thus, the total cost to carpet the room is to the nearest dollar:
J. \$594
