Let P be the original price, then we have the following relationship
[tex]200=P-0.45P[/tex]where 0.45 correspond to 45%. From this equation, we have
[tex]\begin{gathered} 200=P(1-0.45) \\ 200=P(0.55) \end{gathered}[/tex]in which we factorized P. Now, if we move 0.55 to the left hand side, we obtain
[tex]\begin{gathered} \frac{200}{0.55}=P \\ 363.6363=P \end{gathered}[/tex]in other words, the original price was $363.6363. By rounding up to the nearest cent, we have $363.64