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2.4 Divide 240 g in the ratio \( 5: 3: 4 \). 2.5 Brooklyn earns R35 540 per month. She splits her earnings into the ratio \( 2: 6 \) and saves the smaller amount. How much of her earnings does she spend? 2.6 A municipality has budgeted R 80000 for putting up new street name boards. The street name boards cost R 134 each. How many new street name boards can be put up, and how much money will be left in the budget? 2.7 The price of petrol increased from \( \mathrm{R} 12,58 \) per litre to R 13,28 per litre. Determine the percentage increase in price. 2.8 If Luke can consistently run 80 m in 16 s : 2.8.1 How long will it take him to run 400 m ? 2.8.2 How far can Luke run in 1 minute and 4 seconds? 2.9 My car can travel 10 km on every litre of petrol. How much petrol will I need to drive 400 km ?

Ask by Christensen Marshall. in South Africa
Mar 12,2025

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Answer

**2.4** The amounts are 100 g, 60 g, and 80 g. --- **2.5** Brooklyn spends R26,655. --- **2.6** 597 new street name boards can be put up, with R2 left in the budget. --- **2.7** The price increased by approximately 5.56%. --- **2.8** *2.8.1* It will take Luke 80 seconds to run 400 m. *2.8.2* Luke can run 320 m in 1 minute and 4 seconds. --- **2.9** 40 litres of petrol are needed to drive 400 km.

Solution

**2.4** Let the common factor be \( x \). The ratio \( 5:3:4 \) implies the amounts are \[ 5x,\quad 3x,\quad 4x. \] Since the total mass is 240 g, we have \[ 5x + 3x + 4x = 12x = 240. \] Solving for \( x \): \[ x = \frac{240}{12} = 20. \] Thus, the amounts are: \[ 5x = 5 \times 20 = 100\text{ g},\quad 3x = 3 \times 20 = 60\text{ g},\quad 4x = 4 \times 20 = 80\text{ g}. \] --- **2.5** Brooklyn splits her earnings of R35 540 in the ratio \( 2:6 \). The total number of parts is \[ 2 + 6 = 8. \] Each part is \[ \frac{35540}{8} = 4442.5. \] Since she saves the smaller amount (2 parts), her savings are \[ 2 \times 4442.5 = 8885. \] Therefore, the amount she spends (6 parts) is \[ 6 \times 4442.5 = 26655. \] --- **2.6** The municipality has a budget of R80000 and each street name board costs R134. To find the number of boards that can be put up, divide the budget by the cost per board: \[ \text{Number of boards} = \left\lfloor \frac{80000}{134} \right\rfloor. \] Calculating: \[ 134 \times 597 = 79998. \] Since \( 134 \times 598 = 80132 \) (which exceeds the budget), the municipality can put up 597 boards. The remaining budget is \[ 80000 - 79998 = 2. \] --- **2.7** The price of petrol increased from R12.58 to R13.28. The increase is \[ 13.28 - 12.58 = 0.70. \] The percentage increase is given by \[ \frac{0.70}{12.58} \times 100 \approx 5.56\%. \] --- **2.8** Luke runs 80 m in 16 s, so his speed is \[ \frac{80}{16} = 5 \text{ m/s}. \] *2.8.1* To run 400 m, the time required is \[ \text{Time} = \frac{400}{5} = 80 \text{ s}. \] *2.8.2* 1 minute and 4 seconds is \[ 60 + 4 = 64 \text{ s}. \] The distance he can run in 64 s is \[ 5 \times 64 = 320 \text{ m}. \] --- **2.9** If the car can travel 10 km per litre, then to cover 400 km, the required petrol is \[ \frac{400}{10} = 40 \text{ litres}. \]

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Bonus Knowledge

To divide 240 g in the ratio \(5:3:4\), first add the parts of the ratio together: \(5 + 3 + 4 = 12\). Each part then equals \( \frac{240}{12} = 20\) g. Therefore, the proportions are \(5 \times 20 = 100\) g, \(3 \times 20 = 60\) g, and \(4 \times 20 = 80\) g. Brooklyn's earnings of R35 540 divided in the ratio \(2:6\) means that the total parts are \(2 + 6 = 8\). The portion she takes is \( \frac{2}{8} \times 35 540 = R8 885\), which leaves her with \(R35 540 - R8 885 = R26 655\) to spend!

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