Final answer:
The cost to carpet a 10 feet by 12 feet room with carpet costing $12.51 per square yard is approximately $166.50, after converting the room's area from square feet to square yards and multiplying by the carpet price per square yard.
Step-by-step explanation:
To calculate the cost of carpeting a room, one must first determine the area of the room in the appropriate units. Since carpet pricing is usually per square yard, the area of the room should also be calculated in square yards. Given that the room is 10 feet wide and 12 feet long, we first calculate the area in square feet and then convert to square yards.
The area in square feet = width × length = 10 ft × 12 ft = 120 sq ft.
Since there are 9 square feet in a square yard, we divide the total area in square feet by 9 to convert to square yards:
Area in square yards = 120 sq ft × (1 sq yd / 9 sq ft) = 13.33 sq yd (rounded to two decimal places).
The cost can then be calculated by multiplying the area in square yards by the price per square yard of the carpet:
Cost = area in sq yd × price per sq yd = 13.33 sq yd × $12.51/sq yd = $166.50 (rounded to two decimal places).
The final cost to carpet the room with the given dimensions will be approximately $166.50, assuming there are no additional costs for installation or wastage.