Final answer:
The Smith family room requires 70 square yards of carpeting, and the total cost for the carpeting at $13 per square yard will be $910.
Step-by-step explanation:
To calculate the number of square yards the Smith family will need for their family room, which is 30 feet long and 21 feet wide, we must first find the area in square feet and then convert it to square yards since carpeting is typically sold by the square yard.
First, we calculate the area in square feet:
Area = Length × Width
Area = 30 ft × 21 ft
Area = 630 sq ft
Now, since there are 9 square feet in 1 square yard, we convert the area to square yards:
Square yards = Area in square feet ÷ 9
Square yards = 630 sq ft ÷ 9
Square yards = 70 sq yd
Next, to calculate the total cost for the carpeting, we need to multiply the area in square yards by the cost per square yard:
Total cost = Square yards × Cost per square yard
Total cost = 70 sq yd × $13/ sq yd
Total cost = $910
The Smith family will need 70 square yards of carpeting and will spend a total of $910.