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Calculate the water bill for 33 kl based on a tiered pricing structure, excluding VAT.

Mathematics

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Answers

2 parts
a

R 408.92\text{R } 408.92

b

R 470.26\text{R } 470.26

Step-by-step solution

8 steps

To calculate the water bill for 33 kl, we need to apply the tiered pricing structure provided in the table.

Part a· 5 steps

excluding VAT

  1. Calculate the cost for the first 9 kl (0 kl to 9 kl).

    The rate for this tier is R 9.50 per kl.

    Cost1=9 kl×R 9.50/kl=R 85.50\text{Cost}_1 = 9 \text{ kl} \times \text{R } 9.50/\text{kl} = \text{R } 85.50

  2. Calculate the cost for the next 16 kl (from 9 kl to 25 kl).

    The volume in this tier is 25 kl−9 kl=16 kl25 \text{ kl} - 9 \text{ kl} = 16 \text{ kl}.
    The rate for this tier is R 11.22 per kl.

    Cost2=16 kl×R 11.22/kl=R 179.52\text{Cost}_2 = 16 \text{ kl} \times \text{R } 11.22/\text{kl} = \text{R } 179.52

  3. Calculate the cost for the next 5 kl (from 25 kl to 30 kl).

    The volume in this tier is 30 kl−25 kl=5 kl30 \text{ kl} - 25 \text{ kl} = 5 \text{ kl}.
    The rate for this tier is R 14.95 per kl.

    Cost3=5 kl×R 14.95/kl=R 74.75\text{Cost}_3 = 5 \text{ kl} \times \text{R } 14.95/\text{kl} = \text{R } 74.75

  4. Calculate the cost for the remaining 3 kl (from 30 kl to 33 kl).

    The total consumption is 33 kl. The volume already accounted for is 9+16+5=30 kl9 + 16 + 5 = 30 \text{ kl}.
    The remaining volume is 33 kl−30 kl=3 kl33 \text{ kl} - 30 \text{ kl} = 3 \text{ kl}.
    This falls into the "from 30 kl to 45 kl" tier, with a rate of R 23.05 per kl.

    Cost4=3 kl×R 23.05/kl=R 69.15\text{Cost}_4 = 3 \text{ kl} \times \text{R } 23.05/\text{kl} = \text{R } 69.15

  5. Sum all costs to find the total bill excluding VAT.

    Total excluding VAT=Cost1+Cost2+Cost3+Cost4\text{Total excluding VAT} = \text{Cost}_1 + \text{Cost}_2 + \text{Cost}_3 + \text{Cost}_4 Total excluding VAT=R 85.50+R 179.52+R 74.75+R 69.15=R 408.92\text{Total excluding VAT} = \text{R } 85.50 + \text{R } 179.52 + \text{R } 74.75 + \text{R } 69.15 = \text{R } 408.92

    The water bill excluding VAT is R 408.92\boxed{\text{R } 408.92}.

Part b

R 470.26\text{R } 470.26

including VAT

  1. Assume a VAT rate.

    Since the currency is R (South African Rand) and no VAT rate is provided, we will assume the standard South African VAT rate of 15%.

  2. Calculate the VAT amount.

    VAT amount=Total excluding VAT×VAT rate\text{VAT amount} = \text{Total excluding VAT} \times \text{VAT rate} VAT amount=R 408.92×0.15=R 61.338\text{VAT amount} = \text{R } 408.92 \times 0.15 = \text{R } 61.338

    Rounding to two decimal places, the VAT amount is R 61.34.

  3. Calculate the total bill including VAT.

    Total including VAT=Total excluding VAT+VAT amount\text{Total including VAT} = \text{Total excluding VAT} + \text{VAT amount} Total including VAT=R 408.92+R 61.34=R 470.26\text{Total including VAT} = \text{R } 408.92 + \text{R } 61.34 = \text{R } 470.26

    The water bill including VAT is R 470.26\boxed{\text{R } 470.26}.

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