1. **State the problem:** We need to find the starting value of Hattie's house given that after one year it increased by 9%, and after the second year it decreased by 4%, resulting in a value of 287760. 2. **Define variables and formulas:** Let the starting value be $x$. After one year, the value increases by 9%, so the value is: $$x \times (1 + 0.09) = 1.09x$$ After the second year, the value decreases by 4%, so the value is: $$1.09x \times (1 - 0.04) = 1.09x \times 0.96 = 1.0464x$$ 3. **Set up the equation:** We know the value after two years is 287760, so: $$1.0464x = 287760$$ 4. **Solve for $x$:** $$x = \frac{287760}{1.0464}$$ 5. **Calculate the value:** $$x = 274999.999 \approx 275000$$ 6. **Interpretation:** The starting value of the house was approximately 275000. **Final answer:** $$\boxed{275000}$$