Answer
The cost of carpeting the bedrooms is\[\$933.40\].
Work Step by Step
To calculate the cost of carpeting the three rooms, we will first find the area of the three bedrooms.
Compute the area of the master bedroom as follows:
\[\begin{align}
& {{A}_{1}}=lb \\
& =14\text{ ft}\times 14\text{ ft} \\
& =196\text{ f}{{\text{t}}^{2}}
\end{align}\]
Compute the area of the second bedroom as follows:
\[\begin{align}
& {{A}_{2}}=lb \\
& =11\text{ ft}\times 12\text{ ft} \\
& =132\text{ f}{{\text{t}}^{2}}
\end{align}\]
Compute the area of the second bedroom as follows:
\[\begin{align}
& {{A}_{3}}=lb \\
& =12\text{ ft}\times 11\text{ ft} \\
& =132\text{ f}{{\text{t}}^{2}}
\end{align}\]
Compute the total area of all the bedrooms as follows:
\[\begin{align}
& \text{Total area}={{A}_{1}}+{{A}_{2}}+{{A}_{3}} \\
& =\text{196 f}{{\text{t}}^{2}}+132\text{ f}{{\text{t}}^{2}}+132\text{ f}{{\text{t}}^{2}} \\
& =460\text{ f}{{\text{t}}^{2}}
\end{align}\]
It is known that\[\text{1 f}{{\text{t}}^{2}}=\frac{1}{9}\text{ y}{{\text{d}}^{2}}\], convert total area into square yard as follows:
\[\begin{align}
& 460\text{ f}{{\text{t}}^{2}}=460\text{ }f{{t}^{2}}\times \frac{1\text{ y}{{\text{d}}^{2}}}{9f{{t}^{2}}} \\
& =\frac{460}{9}\text{y}{{\text{d}}^{2}} \\
& =51.1\text{ y}{{\text{d}}^{2}} \\
& \simeq 52\text{ y}{{\text{d}}^{2}}
\end{align}\]
Compute the cost of carpeting these rooms as follows:
\[\begin{align}
& \text{Cost}=\$17.95\times52\text{y}{{\text{d}}^{2}}\\&=\$933.40\end{align}\]
Hence, the cost of carpeting the bedrooms is\[\$933.40\].
