1. **State the problem:** Winifred bought a bib necklace at a 45% discount, saving $63. We need to find the original price of the necklace. 2. **Formula and explanation:** The discount amount is calculated as a percentage of the original price. If $P$ is the original price, then the discount is $0.45P$. 3. **Set up the equation:** Since the discount saved her $63, we have: $$0.45P = 63$$ 4. **Solve for $P$:** Divide both sides by 0.45: $$P = \frac{63}{0.45}$$ 5. **Show cancellation:** $$P = \frac{63}{\cancel{0.45}} \times \frac{\cancel{1}}{1}$$ 6. **Calculate:** $$P = 140$$ 7. **Answer:** The original price of the necklace was $140.