Answer
If the cost of the smaller building is known, the increase in the cost for building the larger building will be\[\$x\left(\frac{5}{4}\right)\].
Work Step by Step
The cost of building the area \[8\text{ft}\text{.}\times 10\text{ft}\text{.}=80\text{ft}{{\text{.}}^{\text{2}}}\] is $x.
The increased area is\[12\text{ ft}\times 15\text{ ft}=180\text{ f}{{\text{t}}^{\text{2}}}\].
\[\text{Cost for 1f}{{\text{t}}^{\text{2}}}=\frac{\$x}{80}\]
Computation of the cost for \[180\text{ f}{{\text{t}}^{2}}\]is as follows:
\[\begin{align}
& \text{Cost for 180f}{{\text{t}}^{\text{2}}}=\frac{\$x}{\cancel{80}}\times\cancel{180}\\&\text{}=\frac{9}{4}\times\$x\\\end{align}\]
Since area increases by,\[180\text{ f}{{\text{t}}^{\text{2}}}-80\text{ f}{{\text{t}}^{\text{2}}}=100\text{ f}{{\text{t}}^{\text{2}}}\],the increase in the cost will be the cost for 100ft2.
Compute the increase in cost as follows;
\[\begin{align}
& \text{Increase in cost}=\frac{9}{4}\times \$x-\$x\\&=\$x\left(\frac{9}{4}-1\right)\\&=\$x\left(\frac{5}{4}\right)\end{align}\]
Hence, if the cost of the smaller building is known, the increase in the cost for building the larger building will be\[\$x\left(\frac{5}{4}\right)\].
