1. The problem involves solving the equation $$111 + 48 = 1 \frac{46}{1} + 13$$ where the mixed number is $$1 \frac{46}{1}$$ which simplifies to $$1 + 46 = 47$$. 2. First, simplify the left side: $$111 + 48 = 159$$ 3. Simplify the right side: $$1 \frac{46}{1} + 13 = 47 + 13 = 60$$ 4. The equation becomes: $$159 = 60$$ which is not true, so the original equation as stated is inconsistent. 5. The second equation is: $$245 + 16 = x + 34$$ 6. Simplify the left side: $$245 + 16 = 261$$ 7. To find $$x$$, subtract 34 from both sides: $$261 = x + 34$$ $$\cancel{261} = x + \cancel{34}$$ $$x = 261 - 34$$ 8. Calculate: $$x = 227$$ Final answer: $$x = 227$$