Answer: First, let's convert the room's dimensions from feet to yards, since the carpet cost is given per square yard:
17 feet = 5.67 yards (rounded to two decimal places)
16 feet = 5.33 yards (rounded to two decimal places)
Next, we can calculate the area of the room in square yards by multiplying these values:
Area = 5.67 yards × 5.33 yards = 30.23 square yards (rounded to two decimal places)
Finally, we can multiply the area by the cost per square yard to get the total cost:
Total cost = 30.23 square yards × $101/square yard = $3,056.23 (rounded to two decimal places)
Therefore, it will cost $3,056.23 to carpet the room.