Rewrite 92 and 146 as products of their prime factors. Write down the LCM and HCF of 92 and 146 . Divide 240 g in the ratio \( 5: 3: 4 \). Thoriso can either walk to school at \( 5 \mathrm{~km} / \mathrm{h} \) or ride her bicycle at \( 15 \mathrm{~km} / \mathrm{t} \) If she rides her bicycle, it takes her 10 minutes to get to school. 2.4.1. How long will it take her if she walks to school? 2.4.2. Is this direct or indirect proportion? Give a reason for your answe Brian wants to exchange South-African rand for British pound. If R1 is worth 0,075199 pound, how many pounds will he get for R2 100 if he must pay an agent commission of \( 1,5 \% \) ? The price of petrol is increased from R12,58 per litre to \( \mathrm{R} 13,28 \) per litre. Determine the percentage increase in the price. A motor car drives at an average speed of \( 106 \mathrm{~km} / \mathrm{h} \) for 2 hours 45 minut At which constant speed must the car drive to travel the same distance ir 2 hours 35 minutes?

Below is one complete solution with clear explanations for each part. ────────────────────────────── 1. Prime Factorisation, LCM and HCF of 92 and 146 a) Rewrite 92 and 146 as products of their prime factors. •  92 = 2 × 46 = 2 × (2 × 23) = 2² × 23 •  146 = 2 × 73 b) Find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of 92 and 146. •  HCF: Look at the common prime factors.   Both 92 and 146 have a factor of 2.   Thus, HCF = 2. •  LCM: Take each prime factor at its highest power from either number.   For 2, the highest power is 2² (from 92); for 23 it appears only in 92; for 73 it appears only in 146.   Thus, LCM = 2² × 23 × 73   First calculate 2² = 4, then 4 × 23 = 92, and finally 92 × 73 = 6716.   So, LCM = 6716. ────────────────────────────── 2. Divide 240 g in the ratio 5 : 3 : 4 •  Total parts = 5 + 3 + 4 = 12 •  First part: (5/12) × 240 = 100 g •  Second part: (3/12) × 240 = 60 g •  Third part: (4/12) × 240 = 80 g ────────────────────────────── 3. Thoriso’s Journey to School Thoriso may either walk at 5 km/h or ride her bicycle at 15 km/h. If she rides her bicycle, it takes her 10 minutes to get to school. Step 1. Calculate the distance to school.   Time riding = 10 minutes = 10/60 = 1/6 hour   Distance = Speed × Time = 15 km/h × (1/6 h) = 15/6 = 2.5 km 2.4.1. How long will it take her if she walks to school?   Walking speed = 5 km/h   Time = Distance / Speed = 2.5 km / 5 km/h = 0.5 hour = 30 minutes 2.4.2. Is this direct or indirect proportion? Give a reason for your answer.   Answer: It is an indirect proportion because for a fixed distance, the time taken is inversely proportional to the speed. In other words, if the speed increases, the time taken decreases, and vice versa. ────────────────────────────── 4. Currency Exchange Calculation Brian wants to exchange South-African rand (R) for British pounds (£). Given: R1 = £0.075199 and he has R2100. An agent commission of 1.5% is charged. Step 1. Calculate the amount in pounds before commission.   Pounds = R2100 × 0.075199   = 2100 × 0.075199   ≈ £157.92 Step 2. Deduct the agent’s commission.   Commission = 1.5% of £157.92   = 0.015 × 157.92   ≈ £2.37 Step 3. Net amount received = £157.92 – £2.37   ≈ £155.55 ────────────────────────────── 5. Percentage Increase in the Price of Petrol The price of petrol increases from R12.58 per litre to R13.28 per litre. Step 1. Find the increase in price:   Increase = 13.28 – 12.58 = R0.70 Step 2. Calculate the percentage increase:   Percentage Increase = (Increase / Original Price) × 100   = (0.70 / 12.58) × 100   ≈ 5.56% ────────────────────────────── 6. Finding the Required Constant Speed A motor car drives at an average speed of 106 km/h for 2 hours 45 minutes. Step 1. Convert the time to hours.   2 hours 45 minutes = 2 + (45/60) = 2 + 0.75 = 2.75 hours Step 2. Calculate the distance traveled.   Distance = Speed × Time = 106 km/h × 2.75 h   = 106 × 2 + 106 × 0.75   = 212 + 79.5   = 291.5 km Step 3. Determine the constant speed needed to cover 291.5 km in 2 hours 35 minutes.   Convert 2 hours 35 minutes to hours:   2 hours 35 minutes = 2 + (35/60) ≈ 2 + 0.5833 = 2.5833 hours   Required speed = Distance / Time = 291.5 km / 2.5833 h   ≈ 112.8 km/h ────────────────────────────── Summary of Answers 1. For 92 and 146:   92 = 2² × 23, 146 = 2 × 73   HCF = 2, LCM = 6716 2. Dividing 240 g:   100 g, 60 g, and 80 g 3. Thoriso’s journey:   Walking time = 30 minutes   The relationship is an indirect proportion (time is inversely proportional to speed). 4. Currency exchange:   Brian receives approximately £155.55. 5. Petrol price increase:   Approximately 5.56% 6. Constant speed required:   Approximately 112.8 km/h These are the detailed solutions for each part of the problem.