Subjects algebra

Water Tariff Calculation

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1. **State the problem:** Calculate the total amount Bong'i has to pay for water usage based on the tariffs and quantities given, including 15% VAT. 2. **Given data:** - Bracket 1: 6.110 kilolitres @ 16.929000 per kilolitre - Bracket 2: 4.073 kilolitres @ 10.323610 per kilolitre - Bracket 3: 2.871 kilolitres @ 24.063710 per kilolitre - VAT = 15% 3. **Formula:** Total amount before VAT = \(\sum (\text{quantity} \times \text{rate})\) Amount including VAT = Total before VAT \times (1 + \text{VAT rate}) 4. **Calculate amount before VAT:** - Bracket 1: \(6.110 \times 16.929000 = 103.44119\) - Bracket 2: \(4.073 \times 10.323610 = 42.05668\) - Bracket 3: \(2.871 \times 24.063710 = 69.08344\) Sum before VAT = \(103.44119 + 42.05668 + 69.08344 = 214.58131\) 5. **Calculate amount including VAT:** \[\text{Total with VAT} = 214.58131 \times 1.15 = 246.7685\] 6. **Compare with given answers:** - Kurt-Lee's answer: 263.48 - Damian's answer: 258.48 Our calculated amount including VAT is \(246.77\), which is less than both answers. 7. **Check if VAT was applied correctly:** If VAT was applied only on the total amount, our calculation is correct. 8. **Conclusion:** Neither Kurt-Lee nor Damian's answers match the calculated total including VAT of \(246.77\). Therefore, Bong'i's claim that Damian was correct is **not** supported by the calculations. **Final answer:** \(\boxed{246.77}\) is the correct amount Bong'i has to pay including VAT.