1. **Stating the problem:** We have several tables and number lines showing relationships between quantities and their percent values. The goal is to find missing values marked as "?" in these tables and diagrams. 2. **Understanding percent problems:** Percent problems relate a part to a whole using the formula: $$\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100$$ or equivalently, $$\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}$$ and $$\text{Whole} = \frac{\text{Part} \times 100}{\text{Percent}}$$ 3. **Solving the Number of Trees table:** Given: - Number of Trees: 9, 1, ? - Percent Value: 36, 2, 62 - Total Percent: 100 Find the missing number of trees corresponding to 62%. Using the formula: $$\text{Whole} = 9 + 1 + x = 10 + x$$ Percent for missing part is 62%, so: $$62 = \frac{x}{10 + x} \times 100$$ Divide both sides by 100: $$\frac{62}{100} = \frac{x}{10 + x}$$ Cross multiply: $$62(10 + x) = 100x$$ Distribute: $$620 + 62x = 100x$$ Subtract 62x from both sides: $$620 = 100x - 62x = 38x$$ Divide both sides by 38: $$x = \frac{620}{38}$$ Simplify fraction: $$x = \frac{\cancel{620}^{31} \times 20}{\cancel{38}^{19} \times 2} = \frac{31 \times 20}{19 \times 2} = \frac{620}{38} = 16.3158...$$ Since number of trees must be whole, approximate to 16. 4. **Solving the Number of People table:** Given: - Number of People: 8, 1, ? - Percent Value: 16, ?, 100 First, find the missing percent for 1 person: Sum of known percents: 16 + ? + ? = 100 We know total percent is 100, so the missing percent for 1 person is: $$\text{Percent for 1 person} = \frac{1}{8 + 1 + x} \times 100$$ But we don't know x or the percent for the last group. Since the problem is incomplete here, we cannot solve further without more data. 5. **Students number line and percent:** Given a number line from 0 to 110 students and a percent line from 0 to 100%, with 20% shaded representing 57 minutes. To find the total movie length (100%), use the proportion: $$\frac{20}{100} = \frac{57}{x}$$ Cross multiply: $$20x = 5700$$ Divide both sides by 20: $$x = \frac{5700}{20} = 285$$ So, the total movie length is 285 minutes. 6. **Summary:** - Number of Trees missing value is approximately 16. - Total movie length is 285 minutes. - Other missing values require more data.