Question

Joyce paid $200 for an item at the store that was 45 percent of the original price. What was the original price?

Answer 1

Let P be the original price, then we have the following relationship

`200=P-0.45P`

where 0.45 correspond to 45%. From this equation, we have

`\begin{gathered} 200=P(1-0.45) \\ 200=P(0.55) \end{gathered}`

in which we factorized P. Now, if we move 0.55 to the left hand side, we obtain

`\begin{gathered} (200)/(0.55)=P \\ 363.6363=P \end{gathered}`

in other words, the original price was $363.6363. By rounding up to the nearest cent, we have $363.64