1. **Problem 216:** Given that Newspaper A sells for $1.00 and Newspaper B sells for $1.25, let the number of copies sold of A be $x$ and of B be $y$. 2. The total number of newspapers sold is $x + y$. 3. The percentage $p$ of newspapers sold that are Newspaper A is given by: $$p = \frac{x}{x + y} \times 100$$ 4. The total revenue is: $$R = 1.00x + 1.25y$$ 5. The revenue from Newspaper A is $1.00x$, so the percentage $r$ of revenue from Newspaper A is: $$r = \frac{1.00x}{1.00x + 1.25y} \times 100$$ 6. Express $y$ in terms of $x$ and $p$ from step 3: $$p = \frac{x}{x + y} \times 100 \implies \frac{p}{100} = \frac{x}{x + y} \implies x + y = \frac{100x}{p} \implies y = \frac{100x}{p} - x = x\left(\frac{100}{p} - 1\right)$$ 7. Substitute $y$ into the revenue expression for $r$: $$r = \frac{x}{x + 1.25y} \times 100 = \frac{x}{x + 1.25 \times x \left(\frac{100}{p} - 1\right)} \times 100 = \frac{x}{x + 1.25x \left(\frac{100 - p}{p}\right)} \times 100$$ 8. Factor $x$ out: $$r = \frac{x}{x \left(1 + 1.25 \frac{100 - p}{p}\right)} \times 100 = \frac{1}{1 + 1.25 \frac{100 - p}{p}} \times 100$$ 9. Simplify the denominator: $$1 + 1.25 \frac{100 - p}{p} = \frac{p}{p} + \frac{1.25(100 - p)}{p} = \frac{p + 125 - 1.25p}{p} = \frac{125 - 0.25p}{p}$$ 10. So, $$r = \frac{100}{\frac{125 - 0.25p}{p}} = 100 \times \frac{p}{125 - 0.25p}$$ 11. Multiply numerator and denominator by 4 to clear decimals: $$r = \frac{400p}{500 - p}$$ 12. The correct answer is option D. --- 13. **Problem 217:** The average production for $n$ days is 50 units. 14. Total production for $n$ days is: $$50n$$ 15. Today's production is 90 units, and the new average after $n+1$ days is 55 units. 16. Total production after $n+1$ days is: $$50n + 90$$ 17. The new average is: $$\frac{50n + 90}{n + 1} = 55$$ 18. Multiply both sides by $n+1$: $$50n + 90 = 55(n + 1) = 55n + 55$$ 19. Rearrange: $$50n + 90 = 55n + 55 \implies 90 - 55 = 55n - 50n \implies 35 = 5n \implies n = 7$$ 20. The correct answer is option E. **Final answers:** - Problem 216: D. $\displaystyle \frac{400p}{500 - p}$ - Problem 217: E. 7