1. Problem 6: On a map, 1 inch represents 20 miles. The distance between 2 towns is 6\frac{1}{5} inches. Find the actual distance in miles. 2. Convert mixed fraction 6\frac{1}{5} to improper fraction: $$6\frac{1}{5} = \frac{31}{5}$$ 3. Calculate actual distance by multiplying map distance by scale: $$\text{Distance} = \frac{31}{5} \times 20 = \frac{31 \times 20}{5} = \frac{620}{5} = 124$$ miles 4. So, the actual distance between the two towns is 124 miles. 5. Problem 7: Calculate weighted average of student marks with weights: Mathematics 3, English 3, History 2, Science 2, Art 1. 6. Given marks: - Geometry (Math): 89 - American Literature (English): 92 - American History (History): 94 - Biology (Science): 81 - Sculpture (Art): 85 7. Multiply each mark by its weight: $$89 \times 3 = 267$$ $$92 \times 3 = 276$$ $$94 \times 2 = 188$$ $$81 \times 2 = 162$$ $$85 \times 1 = 85$$ 8. Sum weighted scores: $$267 + 276 + 188 + 162 + 85 = 978$$ 9. Sum of weights: $$3 + 3 + 2 + 2 + 1 = 11$$ 10. Calculate weighted average: $$\frac{978}{11} = 88.91$$ (rounded to two decimals) Hence, the student's weighted average is approximately 88.91.