Question 2. Use the table to answer the questions that follow: 2.1 Define the concept basic charge in the given context. 2.2 Show how the tariff of R18, 87 during the 2017/2018 per... Question 2. Use the table to answer the questions that follow: 2.1 Define the concept basic charge in the given context. 2.2 Show how the tariff of R18, 87 during the 2017/2018 period was calculated. 2.3 A certain household has received a bill of R205, 24 at the end of August 2018. Use the tariffs table above to calculate the number of kilolitres of water the household consumed. 2.4 Mangaung local municipality has introduced a prepaid system of paying water. On the 01/09/2018, Mrs Mnisi loaded 133kl of water and on the 15/09/2018 when she checked the meter readings, only 53,7kl of water was remaining. Determine the amount of water she has used thus far. Read more

Steps to Solve

1. Define basic charge

In this context, 'basic charge' refers to a fixed monthly fee that is charged to all residential water users, regardless of the amount of water consumed. It covers the fixed costs associated with providing water services, such as infrastructure maintenance and administrative expenses.

2. Show the calculation of the tariff of R18,87

The tariff of R18,87 is the price per kiloliter ($kl$) for water consumption between 16-30 $kl$ during the 2017/2018 period. It was calculated by increasing the 2016/2017 tariff (R17,00) by 11%.

Calculation: $$ \text{New tariff} = \text{Old tariff} + (\text{Percentage increase} \times \text{Old tariff}) $$ $$ \text{New tariff} = 17.00 + (0.11 \times 17.00) $$ $$ \text{New tariff} = 17.00 + 1.87 = 18.87 $$

3. Calculate water consumption based on the bill amount

The bill amount is R205,24. We need to account for basic charge first, then the stepped tariffs to find the kiloliters consumed. Since the bill is for August 2018, we use the 2017/2018 tariffs. The basic charge for 2017/2018 is R24,64. Subtract this from the total bill:

$$ \text{Amount for water usage} = \text{Total bill} - \text{Basic charge} $$ $$ \text{Amount for water usage} = 205.24 - 24.64 = 180.60 $$

Now, we calculate the water consumption based on the step tariffs:

• 0-6 $kl$: R7,46 per $kl$. Cost for 6 $kl$ = $6 \times 7.46 = R44.76$
• 7-15 $kl$: R17,39 per $kl$. This means 9 $kl$ at this rate, Cost for 9 $kl$ = $9 \times 17.39 = R156.51$ The total for the first 15kl is $44.76 + 156.51 = R201.27$. This is more than R180.60, so the consumption is between 7 and 15 $kl$

Let $x$ be the kiloliters used within the 7-15 $kl$ range $44.76 + 17.39x = 180.60$, where $x$ is the amount of kiloliters in the 7-15kl range $17.39x = 180.60 - 44.76 = 135.84$ $x = \frac{135.84}{17.39} = 7.8113 \approx 7.81$

Total kiloliters consumed = 6 + 7.81 = 13.81 $kl$

4. Determine the amount of water used

Mrs. Mnisi loaded 133 $kl$ and had 53.7 $kl$ remaining. $$ \text{Water used} = \text{Water loaded} - \text{Water remaining} $$ $$ \text{Water used} = 133 - 53.7 = 79.3 $$ Mrs. Mnisi used 79.3 $kl$ of water.