Sally's salary in 2006 was $\$37,500$. For 2007 she got a salary increase of $x$ percent. For 2008 she got another salary increase of $x$ percent. For 2009 she got a salary decrease of $2x$ percent. Her 2009 salary is $\$34,825$. Suppose instead, Sally had gotten a $2x$ percent salary decrease for 2007, an $x$ percent salary increase for 2008, and an $x$ percent salary increase for 2009. What would her 2009 salary be then?
1. **Understanding the problem:**
   - Sally's salary in 2006: $37,500.
   - 2007 salary increase: $x$ percent.
   - 2008 salary increase: $x$ percent.
   - 2009 salary decrease: $2x$ percent.
   - 2009 salary: $34,825.

2. **Expressing the salary changes mathematically:**
   - An $x$ percent increase in salary is equivalent to multiplying the salary by $\left(1 + \frac{x}{100}\right)$.
   - An $x$ percent decrease in salary is equivalent to multiplying the salary by $\left(1 - \frac{x}{100}\right)$.

3. **Setting up the equation for the given salary changes:**
   - For 2007: Salary becomes $37,500 \left(1 + \frac{x}{100}\right)$.
   - For 2008: Salary becomes $37,500 \left(1 + \frac{x}{100}\right)^2$.
   - For 2009: Salary becomes $37,500 \left(1 + \frac{x}{100}\right)^2 \left(1 - \frac{2x}{100}\right)$.

4. **Using the given final salary to find $x$:**
   \[
   37,500 \left(1 + \frac{x}{100}\right)^2 \left(1 - \frac{2x}{100}\right) = 34,825
   \]

5. **Solving for $x$:**
   - This equation is complex and typically requires numerical methods or iterative approximation to solve for $x$. For the sake of this problem, we assume $x$ is found correctly.

6. **Reversing the order of salary changes:**
   - Suppose Sally had a $2x$ percent salary decrease in 2007, an $x$ percent salary increase in 2008, and an $x$ percent salary increase in 2009.
   - For 2007: Salary becomes $37,500 \left(1 - \frac{2x}{100}\right)$.
   - For 2008: Salary becomes $37,500 \left(1 - \frac{2x}{100}\right) \left(1 + \frac{x}{100}\right)$.
   - For 2009: Salary becomes $37,500 \left(1 - \frac{2x}{100}\right) \left(1 + \frac{x}{100}\right)^2$.

7. **Calculating the new 2009 salary:**
   - Since multiplication is commutative, the order of multiplication does not affect the result:
   \[
   37,500 \left(1 - \frac{2x}{100}\right) \left(1 + \frac{x}{100}\right)^2 = 37,500 \left(1 + \frac{x}{100}\right)^2 \left(1 - \frac{2x}{100}\right)
   \]
   - Given that $37,500 \left(1 + \frac{x}{100}\right)^2 \left(1 - \frac{2x}{100}\right) = 34,825$, it follows that:
   \[
   37,500 \left(1 - \frac{2x}{100}\right) \left(1 + \frac{x}{100}\right)^2 = 34,825
   \]

Conclusion:
\[
\boxed{34,825}
\]