1. **State the problem:** We need to find the new price after applying a 22% discount to the original price of 25. 2. **Formula:** The new price after a discount is given by: $$\text{New Price} = \text{Original Price} \times (1 - \text{Discount Rate})$$ 3. **Apply the values:** $$\text{New Price} = 25 \times (1 - 0.22)$$ 4. **Simplify inside the parentheses:** $$1 - 0.22 = 0.78$$ 5. **Calculate the new price:** $$\text{New Price} = 25 \times 0.78$$ 6. **Multiply:** $$25 \times 0.78 = 19.5$$ 7. **Round to the nearest cent:** The new price is $19.50$. **Final answer:** The new price after a 22% discount is **19.50**.