1. **Problem 218:** A two-digit positive integer has digits $a$ and $b$, so the number is $10a + b$. 2. When digits are reversed, the number becomes $10b + a$. 3. The problem states the difference between the original and reversed number is 27: $$|(10a + b) - (10b + a)| = 27$$ 4. Simplify the absolute difference: $$|9a - 9b| = 27$$ $$9|a - b| = 27$$ 5. Divide both sides by 9: $$|a - b| = 3$$ 6. So, the digits differ by 3. --- 7. **Problem 219:** Two resistors with resistances $x$ and $y$ are connected in parallel. 8. The combined resistance $r$ satisfies: $$\frac{1}{r} = \frac{1}{x} + \frac{1}{y}$$ 9. Find $r$ by taking the reciprocal: $$\frac{1}{r} = \frac{y + x}{xy}$$ $$r = \frac{xy}{x + y}$$ 10. So, the combined resistance $r$ is $\frac{xy}{x + y}$. **Final answers:** - For problem 218, the digits differ by 3 (Option A). - For problem 219, the combined resistance is $\frac{xy}{x + y}$ (Option D).