1. **State the problem:** Winterfield Bike Shop pays 420 for a bicycle and marks up the price by 17.2% to find the retail price. 2. **Formula used:** Retail price = Cost price + Markup amount Markup amount = Cost price \times Markup rate 3. **Calculate the markup amount:** Markup amount = 420 \times \frac{17.2}{100} = 420 \times 0.172 4. **Perform the multiplication:** Markup amount = 72.24 5. **Calculate the retail price:** Retail price = 420 + 72.24 = 492.24 6. **Final answer:** The retail price of the bicycle is 492.24.