#### Explanation:

The formula for determine percent change is: $p = \frac{N - O}{O} \cdot 100$ where $p$ is the percent change, $N$ is the new price, $O$ is the old price. In this problem $p$ and $N$ are provided so we can substitute for these and solve for $O$ while keeping the equation balanced:

$- 10 = \frac{585 - O}{O} \cdot 100$

$- \frac{10}{100} = \frac{585 - O}{O} \cdot \frac{100}{100}$

$- 0.1 = \frac{585 - O}{O}$

$- 0.1 = \frac{585}{O} - \frac{O}{O}$

$- 0.1 = \frac{585}{O} - 1$

$- 0.1 + 1 = \frac{585}{O} - 1 + 1$

$0.9 = \frac{585}{O}$

$\frac{O}{0.9} 0.9 = \frac{585}{O} \frac{O}{0.9}$

$O = \frac{585}{0.9}$

$O = 650$