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# ### Question 2.1: Susan's Water Usage **2.1.1 Explain the concept of a tariff:** A tariff in this context refers to a structured pricing system used to bill consumers based on the amount of water the

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Question: QUESTION 2 2.1 In the first month of living on her own, Susan used 33 kℓ of water. TABLE 1 shows the residential water tariffs including VAT. TABEL 1: NEW RESIDENTIAL AND COMMERCIAL WATER TARIFFS BLOCK TARIFF SUMMARY (IN KILOLITRES) TARIFF (RAND PER KILOLITRE) Block 1 0–6 kℓ R6,65 Block 2 More than 6–20 kℓ R28,24 Block 3 More than 20–40 kℓ R31,79 Block 4 More than 40–60 kℓ R33,62 Block 5 More than 60 kℓ R35,92 [Adapted from www.kimberley.org.za Use the information above to answer the questions that follow. 2.1.1 Explain the concept tariff. (2) 2.1.2 Write down the tariff in block 5. (2) 2.1.3 Calculate the total amount that Suzan paid for 33 kℓ of water. (4) 2.2 In December 2019, Amoti used 690 kWh of energy. TABLE 2 below shows the electricity tariffs for flats / houses in the local municipality where Amoti lives. TABLE 2: ELECTRICITY TARIFFS FOR FLATS / HOUSES Residential Prepaid Proposed c/kWh [VAT incl] Block 1 (≤ 550 kWh) 124,49c Block 2 (> 550 kWh) 141,43c Service Charge (R/month ) R147,74 [Adapted from electricity-tariffs 2018–2019-Johannesburg] Use the information above to answer the questions that follow. 2.2.1 Determine the monthly service charge for a flat of house excluding VAT. (2) 2.2.2 Calculate the amount that Amoti paid for 690 kWh in December 2019. (4)

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Let's address each question step-by-step: ### 2.1 Water Tariffs #### 2.1.1 Explain the concept of "tariff." A tariff is a fixed charge or rate set by an authority for services rendered or items provided, typically by a government or a municipal entity. In the context of utilities such as water and electricity, it refers to the price per unit (e.g., per kiloliter or per kilowatt hour) that consumers must pay for usage. #### 2.1.2 Write down the tariff in block 5. The tariff in Block 5 is R35,92 per kiloliter. #### 2.1.3 Calculate the total amount that Susan paid for 33 kℓ of water. To calculate this, we need to break down Susan's water usage across the relevant tariff blocks: - Block 1: 0–6 kℓ at R6.65/kℓ - Block 2: More than 6–20 kℓ at R28.24/kℓ - Block 3: More than 20–40 kℓ at R31.79/kℓ Susan's consumption of 33 kℓ falls into the first three blocks. 1. First 6 kℓ at R6.65: $6 \, \text{kℓ} \times R6.65/\text{kℓ} = R39.90$ 2. Next 14 kℓ (from 7 kℓ to 20 kℓ) at R28.24: $14 \, \text{kℓ} \times R28.24/\text{kℓ} = R395.36$ 3. Remaining 13 kℓ (from 21 kℓ to 33 kℓ) at R31.79: $13 \, \text{kℓ} \times R31.79/\text{kℓ} = R413.27$ Adding these amounts together: $R39.90 + R395.36 + R413.27 = R848.53$ Therefore, Susan paid a total of R848.53 for 33 kℓ of water. ### 2.2 Electricity Tariffs #### 2.2.1 Determine the monthly service charge for a flat or house excluding VAT. Given the service charge including VAT is R147.74, we need to exclude the VAT (typically 15% in South Africa). Let $$S$$ be the service charge excluding VAT. Then, $S + 0.15S = R147.74$ $1.15S = R147.74$ $S = \frac{R147.74}{1.15} = \frac{147.74}{1.15} = R128.47$ The monthly service charge excluding VAT is R128.47. #### 2.2.2 Calculate the amount that Amoti paid for 690 kWh in December 2019. To calculate this, we need to account for the rates applicable to the two blocks: - Block 1: Up to 550 kWh at 124.49 c/kWh - Block 2: Above 550 kWh at 141.43 c/kWh 1. First 550 kWh at 124.49 c/kWh: $550 \, \text{kWh} \times 124.49 \, \text{c/kWh} = 68469.5 \, \text{c} = 684.695 \, \text{R}$ 2. Remaining 140 kWh (690 kWh - 550 kWh) at 141.43 c/kWh: $140 \, \text{kWh} \times 141.43 \, \text{c/kWh} = 19800.2 \, \text{c} = 198.002 \, \text{R}$ Adding these amounts together: $R684.695 + R198.002 = R882.697$ Therefore, Amoti paid R882.70 for 690 kWh in December 2019 (rounded to two decimal places). Note that any service charge might need to be added if relevant, but it seems to apply only once for the month and is not per kWh consumed.

May 21, 2024, 6:51 a.m.

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