1. **State the problem:** Solve the equation $$\frac{4y}{5} + 6 \frac{9}{12} = 11 \frac{11}{20}$$ for $y$. 2. **Convert mixed numbers to improper fractions:** - $6 \frac{9}{12} = 6 + \frac{9}{12} = \frac{72}{12} + \frac{9}{12} = \frac{81}{12}$ - $11 \frac{11}{20} = 11 + \frac{11}{20} = \frac{220}{20} + \frac{11}{20} = \frac{231}{20}$ 3. **Rewrite the equation:** $$\frac{4y}{5} + \frac{81}{12} = \frac{231}{20}$$ 4. **Find a common denominator to combine terms or isolate $y$:** The denominators are 5, 12, and 20. The least common denominator (LCD) is 60. 5. **Multiply each term by 60 to clear denominators:** $$60 \times \frac{4y}{5} + 60 \times \frac{81}{12} = 60 \times \frac{231}{20}$$ Calculate each term: - $60 \times \frac{4y}{5} = 12 \times 4y = 48y$ - $60 \times \frac{81}{12} = 5 \times 81 = 405$ - $60 \times \frac{231}{20} = 3 \times 231 = 693$ 6. **Rewrite the equation:** $$48y + 405 = 693$$ 7. **Isolate $y$:** $$48y = 693 - 405 = 288$$ 8. **Solve for $y$:** $$y = \frac{288}{48} = 6$$ **Final answer:** $$y = 6$$