1. **State the problem:** We need to find the original bill amount before the 12% tip was added, given the final bill is 51.28. 2. **Formula used:** If the original bill is $x$, then the final bill after adding a 12% tip is given by: $$\text{Final bill} = x + 0.12x = 1.12x$$ 3. **Set up the equation:** $$1.12x = 51.28$$ 4. **Solve for $x$:** $$x = \frac{51.28}{1.12}$$ 5. **Calculate:** $$x = 45.75$$ 6. **Interpretation:** The bill before the 12% tip was added is 45.75. **Final answer:** The bill without the tip is **45.75**.