Cindy was asked by her teacher to subtract 3 from $a$ certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly?

Step 1 (Represent Cindy's Calculation): Let the original number be $x$. Cindy subtracted 9 from $x$ and then divided the result by 3, which gave an answer of 43. We write this as an equation:

Step 2 (Solve for the Original Number x): Multiply both sides by 3:

So the original number is 138.

Step 3 (Compute the Correct Answer): The teacher's original instruction was to subtract 3 from the number and then divide the result by 9. Applying this to $x=138$:

Step 4 (Conclusion): Her answer would have been exactly 15.