1. Problem: Find the cost of 10 kg of tea leaves when 3 kg cost 18. Formula: Cost is directly proportional to weight, so $\frac{Cost_1}{Weight_1} = \frac{Cost_2}{Weight_2}$. Calculation: $\frac{18}{3} = \frac{x}{10} \Rightarrow x = \frac{18 \times 10}{3} = 60$ Answer: Cost of 10 kg tea leaves is 60. 2. Problem: A student reads 6 pages in 10 minutes. How many pages in 30 minutes? Formula: Pages read is proportional to time, $\frac{Pages_1}{Time_1} = \frac{Pages_2}{Time_2}$. Calculation: $\frac{6}{10} = \frac{x}{30} \Rightarrow x = \frac{6 \times 30}{10} = 18$ Answer: Student reads 18 pages in 30 minutes. 3. Problem: Football team scored 10 goals in 4 games. How many in 18 more games? Formula: Goals per game is constant, so $\frac{10}{4} = \frac{x}{18}$. Calculation: $x = \frac{10 \times 18}{4} = 45$ Answer: Team scores 45 goals in 18 games. 4. Problem: 2 cups flour make 12 biscuits. How much for 30 biscuits? Formula: Flour is proportional to biscuits, $\frac{2}{12} = \frac{x}{30}$. Calculation: $x = \frac{2 \times 30}{12} = 5$ Answer: 5 cups of flour needed. 5. Problem: Upload 8 photos in 7.2 minutes. Time for 20 photos? Formula: Time proportional to photos, $\frac{7.2}{8} = \frac{x}{20}$. Calculation: $x = \frac{7.2 \times 20}{8} = 18$ Answer: 18 minutes to upload 20 photos. 6. Problem: Jamil works 36 hours for 172800. Time to earn (i) 96000 (ii) 288000? Rate per hour = $\frac{172800}{36} = 4800$. (i) Time = $\frac{96000}{4800} = 20$ hours. (ii) Time = $\frac{288000}{4800} = 60$ hours. Answer: (i) 20 hours, (ii) 60 hours. 7. Problem: Sarah has 42 CDs weighing 2436 g. (i) Mass of 28 CDs = $\frac{2436}{42} \times 28 = 1624$ g. (ii) Ratio CD to case = 15:43, total mass = 15 + 43 = 58 units. Mass of one CD = $\frac{15}{58} \times \frac{2436}{42} = 15$ g (approx). Answer: (i) 1624 g, (ii) 15 g per CD. 8. Problem: Expenses $E$ proportional to guests $N$. For 30 guests, $E=210$. Find $E$ for 80 guests. Formula: $\frac{210}{30} = \frac{x}{80}$. Calculation: $x = \frac{210 \times 80}{30} = 560$ Answer: Expenses for 80 guests is 560. 9. Problem: Complete tables with direct proportion. (i) $x:1,3,7$; $y:9,?,45$ $\frac{y}{x} = k$ constant. $k = \frac{9}{1} = 9$ For $x=3$, $y=3 \times 9=27$. (ii) $M:10,20,50$; $E:5,?,40$ $k = \frac{5}{10} = 0.5$ For $M=20$, $E=20 \times 0.5=10$. Answer: (i) $y=27$ for $x=3$; (ii) $E=10$ for $M=20$. 10. Problem: Zeb works 36 hours for 17280. Time to earn (i) 96000 (ii) 28800? Rate per hour = $\frac{17280}{36} = 480$. (i) Time = $\frac{96000}{480} = 200$ hours. (ii) Time = $\frac{28800}{480} = 60$ hours. Answer: (i) 200 hours, (ii) 60 hours.