Given that a sofa is on sale for $363, which is 34% less than the regular price.
To determine: The regular price.
Let the regular price be Y. If the regular price is Y, then the 34%regular price would be
[tex]\begin{gathered} P_{\text{less}}=(100-34)\text{ \% of \$Y} \\ P_{\text{less}}=66\text{ \% of Y} \end{gathered}[/tex]
It should be noted that the 34 % less the regular price is the price on sale. Then,
[tex]\begin{gathered} P_{\text{less}}=\text{ \$363} \\ \text{Therefore,} \\ 66\text{ \% of Y = \$363} \\ \frac{66}{100}\times Y=363 \\ \frac{66Y}{100}=363 \\ 66Y=363\times100 \\ 66Y=36300 \\ Y=\frac{36300}{66} \\ Y=550 \end{gathered}[/tex]
Hence, the regular price of the sofa is $550
