1. **State the problem:** 9 years ago, the ratio of Miko's age to her sister's age was 5:7. This year, the ratio is 4:5. We need to find Miko's current age. 2. **Define variables:** Let Miko's age 9 years ago be $5x$ and her sister's age 9 years ago be $7x$ because their ratio was 5:7. 3. **Express current ages:** Since 9 years have passed, Miko's current age is $5x + 9$ and her sister's current age is $7x + 9$. 4. **Use the current ratio:** The current ratio of their ages is 4:5, so $$\frac{5x + 9}{7x + 9} = \frac{4}{5}$$ 5. **Cross multiply:** $$5(5x + 9) = 4(7x + 9)$$ 6. **Expand both sides:** $$25x + 45 = 28x + 36$$ 7. **Rearrange to isolate $x$:** $$25x + 45 - 28x - 36 = 0$$ $$-3x + 9 = 0$$ 8. **Solve for $x$:** $$-3x = -9$$ $$x = \frac{\cancel{-9}}{\cancel{-3}} = 3$$ 9. **Find Miko's current age:** $$5x + 9 = 5(3) + 9 = 15 + 9 = 24$$ **Answer:** Miko is 24 years old now.