1. **State the problem:** We know that the number of cars registered in October is 100%. September had 15% more cars registered than October, so September is 115% of October. November had a 15% decrease from October, so November is 85% of October. The total number of cars registered over the three months is 62,550. 2. **Set variables and write the equation:** Let the number of cars registered in October be $x$. Then, September registrations = $1.15x$ and November registrations = $0.85x$. 3. **Write the total registration equation:** $$x + 1.15x + 0.85x = 62,550$$ 4. **Simplify the equation:** $$ (1 + 1.15 + 0.85)x = 62,550$$ $$ 3x = 62,550$$ 5. **Solve for $x$:** $$x = \frac{62,550}{3}$$ $$x = 20,850$$ 6. **Interpret the result:** The number of cars registered in October is 20,850. **Final answer:** $$\boxed{20,850}$$