1. **State the problem:** We need to divide 121.50 into two parts in the ratio 4:5. 2. **Formula and explanation:** When dividing a quantity in the ratio $a:b$, the total parts are $a+b$. Each part is found by dividing the total quantity by the sum of the ratio parts and then multiplying by each ratio number. 3. **Calculate total parts:** $$4 + 5 = 9$$ 4. **Find the value of one part:** $$\frac{121.50}{9} = 13.50$$ 5. **Calculate each share:** - First part: $$4 \times 13.50 = 54.00$$ - Second part: $$5 \times 13.50 = 67.50$$ 6. **Check:** $$54.00 + 67.50 = 121.50$$ which matches the total amount. **Final answer:** The two parts are 54.00 and 67.50.