4.2 Calculate the value of \( a \) if: (2) 4.3 increase 5200 kg in the ratio \( 2: 5 \) (2) \( \qquad \) 4.4 Share 90 sweets in the following ratio \( 5: 3: 7 \) \( \qquad \) \( \qquad \) \( \qquad \) (3) \( \qquad \) [9] QUESTION 5 5.1 It takes 7 gardeners 8 hours to plant 1680 seedlings on a piece of land. Calculate (in hours and minutes) how long it would take 12 gardeners to plant the same seedlings. \( \qquad \) \( \qquad \) (2) \( \qquad \) 5.2 A car travelling at a constant speed travels 30 km in 15 minutes. How far will it travel in 2 hours 12 minutes if it continues at the same constant speed? \( \qquad \) \( \qquad \)

Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\frac{1680}{7}\right)\times 8}{12}\) - step1: Divide the terms: \(\frac{240\times 8}{12}\) - step2: Multiply the numbers: \(\frac{1920}{12}\) - step3: Reduce the fraction: \(160\) Calculate or simplify the expression \( 90 * (3/15) \). Calculate the value by following steps: - step0: Calculate: \(90\left(\frac{3}{15}\right)\) - step1: Reduce the fraction: \(90\times \frac{1}{5}\) - step2: Reduce the numbers: \(18\times 1\) - step3: Simplify: \(18\) Calculate or simplify the expression \( (30 / (15/60)) * (132) \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{30}{\left(\frac{15}{60}\right)}\right)\times 132\) - step1: Remove the parentheses: \(\left(\frac{30}{\frac{15}{60}}\right)\times 132\) - step2: Reduce the fraction: \(\left(\frac{30}{\frac{1}{4}}\right)\times 132\) - step3: Divide the terms: \(120\times 132\) - step4: Multiply the numbers: \(15840\) Calculate or simplify the expression \( 5200 * (2/5) \). Calculate the value by following steps: - step0: Calculate: \(5200\times \frac{2}{5}\) - step1: Reduce the numbers: \(1040\times 2\) - step2: Multiply the numbers: \(2080\) Calculate or simplify the expression \( 90 * (5/15) \). Calculate the value by following steps: - step0: Calculate: \(90\left(\frac{5}{15}\right)\) - step1: Reduce the fraction: \(90\times \frac{1}{3}\) - step2: Reduce the numbers: \(30\times 1\) - step3: Simplify: \(30\) Calculate or simplify the expression \( 90 * (7/15) \). Calculate the value by following steps: - step0: Calculate: \(90\times \frac{7}{15}\) - step1: Reduce the numbers: \(6\times 7\) - step2: Multiply the numbers: \(42\) Calculate or simplify the expression \( 30 / (15/60) \). Calculate the value by following steps: - step0: Calculate: \(\frac{30}{\left(\frac{15}{60}\right)}\) - step1: Remove the parentheses: \(\frac{30}{\frac{15}{60}}\) - step2: Reduce the fraction: \(\frac{30}{\frac{1}{4}}\) - step3: Multiply by the reciprocal: \(30\times 4\) - step4: Multiply the numbers: \(120\) Let's solve each part of the problem step by step. ### 4.3 Increase 5200 kg in the ratio \( 2: 5 \) To find the increase in weight, we first need to calculate the total parts in the ratio \( 2:5 \): - Total parts = \( 2 + 5 = 7 \) Now, we can find the increase corresponding to the \( 2 \) parts: \[ \text{Increase} = 5200 \times \frac{2}{7} = 2080 \text{ kg} \] ### 4.4 Share 90 sweets in the ratio \( 5: 3: 7 \) First, we calculate the total parts in the ratio \( 5:3:7 \): - Total parts = \( 5 + 3 + 7 = 15 \) Now, we can find the number of sweets for each part: 1. For \( 5 \) parts: \[ \text{Sweets for 5 parts} = 90 \times \frac{5}{15} = 30 \] 2. For \( 3 \) parts: \[ \text{Sweets for 3 parts} = 90 \times \frac{3}{15} = 18 \] 3. For \( 7 \) parts: \[ \text{Sweets for 7 parts} = 90 \times \frac{7}{15} = 42 \] ### QUESTION 5 #### 5.1 Calculate how long it would take 12 gardeners to plant 1680 seedlings. First, we find the total work done in gardener-hours: \[ \text{Total work} = 7 \text{ gardeners} \times 8 \text{ hours} = 56 \text{ gardener-hours} \] Now, we find the time it would take for 12 gardeners: \[ \text{Time} = \frac{56 \text{ gardener-hours}}{12 \text{ gardeners}} = \frac{56}{12} \text{ hours} = 4.67 \text{ hours} \approx 4 \text{ hours and } 40 \text{ minutes} \] #### 5.2 A car travelling at a constant speed travels 30 km in 15 minutes. First, we calculate the speed of the car: \[ \text{Speed} = \frac{30 \text{ km}}{15 \text{ minutes}} = 120 \text{ km/hour} \] Now, we need to find out how far it will travel in \( 2 \) hours and \( 12 \) minutes: - Convert \( 12 \) minutes to hours: \( 12 \text{ minutes} = \frac{12}{60} = 0.2 \text{ hours} \) - Total time = \( 2 + 0.2 = 2.2 \text{ hours} \) Now, we calculate the distance: \[ \text{Distance} = 120 \text{ km/hour} \times 2.2 \text{ hours} = 264 \text{ km} \] ### Summary of Results - Increase in weight: **2080 kg** - Sweets distribution: **30, 18, 42** - Time for 12 gardeners: **4 hours and 40 minutes** - Distance travelled in 2 hours 12 minutes: **264 km**