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The problem involves calculating electricity costs based on different tariff blocks and meter readings. Could you please provide a detailed solution with steps for each calculation?

Mathematics

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Answers

3 parts
2.1

R2,0970\text{R2,0970}

2.2

600 KWh\text{600 KWh}

2.3

425 KWh\text{425 KWh}

Step-by-step solution

8 steps

Part 2.1· 2 steps

  1. Locate the tariff for block 1 in TABLE 1.

    Block 1 is "1 - 100 KWh" with a cost of "209,70c" per KWh.

  2. Convert the tariff from cents to rands.

    Since 1 Rand = 100 cents, divide the cents value by 100.

    Tariff for block 1 in rands=209,70 c100 c/R\text{Tariff for block 1 in rands} = \frac{209,70 \text{ c}}{100 \text{ c/R}} Tariff for block 1 in rands=2,0970 R\text{Tariff for block 1 in rands} = 2,0970 \text{ R}

    The tariff for block 1 in rands is R2,0970\boxed{\text{R2,0970}}.

Part 2.2

600 KWh\text{600 KWh}

  1. Identify the previous and current meter readings from ANNEXURE A.

    Previous Reading (28/02/2023) = 23 901 KWh
    Current Reading (31/03/2023) = 24 501 KWh

  2. Calculate the total KWh used (D) by subtracting the previous reading from the current reading.

    D=Current Reading−Previous ReadingD = \text{Current Reading} - \text{Previous Reading} D=24501 KWh−23901 KWhD = 24501 \text{ KWh} - 23901 \text{ KWh} D=600 KWhD = 600 \text{ KWh}

    The value of D, the amount in kilowatt (KWh) used in March 2023, is 600 KWh\boxed{\text{600 KWh}}.

Part 2.3

425 KWh\text{425 KWh}

  1. Convert the total amount paid from cents to rands.

    Total amount paid = 101 277.5 cents

    Total amount paid in Rands=101277,5 c100 c/R=R1012,775\text{Total amount paid in Rands} = \frac{101277,5 \text{ c}}{100 \text{ c/R}} = \text{R}1012,775
  2. Calculate the cost for each full block of electricity usage based on TABLE 1.

    • Block 1 (1 - 100 KWh): 100 KWh at 209,70c/KWh (R2,0970/KWh) Cost for Block 1 = 100 KWh×R2,0970/KWh=R209,70100 \text{ KWh} \times \text{R}2,0970/\text{KWh} = \text{R}209,70 Remaining amount = R1012,775 - R209,70 = R803,075

    • Block 2 (101 - 400 KWh): This block covers 300 KWh (400 - 100). Tariff is 245,41c/KWh (R2,4541/KWh). Cost for Block 2 = 300 KWh×R2,4541/KWh=R736,23300 \text{ KWh} \times \text{R}2,4541/\text{KWh} = \text{R}736,23 Remaining amount = R803,075 - R736,23 = R66,845

    • Block 3 (401 - 650 KWh): This block covers 250 KWh (650 - 400). Tariff is 267,38c/KWh (R2,6738/KWh). Since the remaining amount (R66,845) is less than the full cost of Block 3 (R2,6738/KWh ×\times 250 KWh = R668,45), only a portion of Block 3 was used.

  3. Calculate the KWh used in the final block.

    KWh used in Block 3 = Remaining amountTariff for Block 3\frac{\text{Remaining amount}}{\text{Tariff for Block 3}}

    KWh used in Block 3=R66,845R2,6738/KWh\text{KWh used in Block 3} = \frac{\text{R}66,845}{\text{R}2,6738/\text{KWh}} KWh used in Block 3=25 KWh\text{KWh used in Block 3} = 25 \text{ KWh}
  4. Sum the KWh from all blocks to find the total KWh used.

    Total KWh used = KWh from Block 1 + KWh from Block 2 + KWh from Block 3
    Total KWh used = 100 KWh+300 KWh+25 KWh100 \text{ KWh} + 300 \text{ KWh} + 25 \text{ KWh}
    Total KWh used = 425 KWh425 \text{ KWh}
    The number of KWh they used for that period is 425 KWh\boxed{\text{425 KWh}}.

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