We are given the current value of the house, which is $165,000. This has already been decreased by 34%, which means that it is only 66% of the original value.
We know this because the original value is 100%. Decreasing it by 34%, we get 66%.
[tex]100\%-34\%=66\%[/tex]In words, we can say that "66% of the original value of the house is $165,000". We can translate this into a mathematical sentence as follows:
[tex]66\%\times N=165,000[/tex]where N is the original value of the house.
We can now solve for N by dividing each side by 66% or 0.66.
[tex]\begin{gathered} 66\operatorname{\%}N=165,000 \\ 0.66\times N=165,000 \\ \\ \frac{0.66N}{0.66}=\frac{165,000}{0.66} \\ \\ N=250,000 \end{gathered}[/tex]So, the original value of the house was $250,000.
