Answer
The cost of tiling the room of dimensions \[12\text{ft}\text{.}\] by\[15\text{ft}\text{.}\] with tiles of dimensions \[3\text{inch}\] by\[2\text{inch}\] will be\[\$518.4\].
Work Step by Step
To find out the cost of tiling, we need to find the number of tiles required to cover the floor area.
For this, we will divide the area of the room floor with the area of one tile. The units of both these areas should be same. It is known that 1 feet is equivalent to 12 inches.
Area of the room floor will be:
\[\begin{align}
& {{A}_{1}}=12\text{ ft}\times 15\text{ ft} \\
& =12\times 12\left( \text{inch} \right)\times 15\times 12\left( \text{inch} \right) \\
& =\text{144 in}\times 180\text{ in} \\
& =\text{25920 in}{{\text{.}}^{\text{2}}}
\end{align}\]
The area of each tile will be:
\[\begin{align}
& {{A}_{2}}=3\text{ in}\times 2\text{ in} \\
& =6\text{ in}{{\text{.}}^{\text{2}}}
\end{align}\]
Compute the number of tiles in the room as follows:
\[\begin{align}
& \frac{{{A}_{1}}}{{{A}_{2}}}=\frac{25920\text{ i}{{\text{n}}^{2}}}{6\text{ i}{{\text{n}}^{2}}} \\
& =4320
\end{align}\]
Compute the cost of tiling the room as follows:
\[\begin{align}
& \text{Cost}=\frac{4320\text{ tiles}\times \$1.20}{10}\\&=\text{}\!\!\$\!\!\text{}518.4\end{align}\]
Hence, the cost of tiling the room of dimensions \[12\text{ft}\text{.}\] by\[15\text{ft}\text{.}\] with tiles of dimensions \[3\text{inch}\] by\[2\text{inch}\] will be\[\$518.4\].
