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 $39 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 the area of the two rectangles

The floor plan can be divided into two rectangles. The first rectangle has dimensions \(11\,\text{ft} \times 11\,\text{ft}\), and the second rectangle has dimensions \(8\,\text{ft} \times 6\,\text{ft}\).

The area of the first rectangle \(A_1 = 11\times11 = 121\,\text{ft}^2\).

The area of the second rectangle \(A_2 = 8\times6 = 48\,\text{ft}^2\).

Step2: Find the total area in square feet

The total area \(A = A_1+A_2 = 121 + 48=169\,\text{ft}^2\).

Step3: Convert square feet to square yards

Since \(9\,\text{ft}^2 = 1\,\text{yd}^2\), the area in square yards \(A_{\text{yd}^2}=\frac{169}{9}\approx 18.78\,\text{yd}^2\).

Step4: Calculate the total cost

The cost per square yard is \(\$39\), so the total cost \(C = 39\times18.78\approx 732.42\). Rounding to the nearest cent, we get \(732.33\) (wait, maybe my approximation in step 3 was different. Let's recalculate step 3 and 4 precisely.

Wait, \(169\div9=\frac{169}{9}\approx18.777\ldots\)

Then \(39\times\frac{169}{9}=\frac{39\times169}{9}=\frac{6591}{9} = 732.333\ldots\), which rounds to \(732.33\).

Answer:

\(732.33\)