Question

you want to install wall-to-wall carpeting in the family room. the floor plan is shown. if the cost of the carpet you would like to purchase is $34 per square yard, what is the cost (in dollars) of carpeting your family room? assume that there is no waste. hint: 9 ft² = 1 yd². (round your answer to the nearest cent.) $

Explanation:

Step1: Calculate area of two rectangles

The floor plan consists of two rectangles. One is \(6\) ft by \(9\) ft, and the other is \(13\) ft by \(13\) ft.
Area of first rectangle: \(A_1 = 6\times9 = 54\) square feet.
Area of second rectangle: \(A_2 = 13\times13 = 169\) square feet.

Step2: Total area in square feet

Total area \(A = A_1 + A_2 = 54 + 169 = 223\) square feet.

Step3: Convert to square yards

Since \(9\) ft² = \(1\) yd², divide total area by \(9\):
\(A_{\text{yd}^2} = \frac{223}{9} \approx 24.7778\) square yards.

Step4: Calculate total cost

Cost per square yard is \$34, so total cost \(C = 34\times24.7778 \approx 842.44\) dollars.

Answer:

\(842.44\)