Sure, let's break down the problems step by step for clarity:
### 1.1.1 Show that the cost for 45 kWh of electricity is R 35.94.
To calculate the cost of using 45 kWh of electricity, we need to use the rate given for the 0-50 kWh range, which is [tex]\( R 0.7986 \)[/tex] per kWh.
[tex]\[
\text{Cost for 45 kWh} = 45 \times 0.7986
\][/tex]
Carrying out the multiplication:
[tex]\[
= 45 \times 0.7986 \approx 35.937
\][/tex]
Rounding 35.937 to two decimal places, we get:
[tex]\[
35.94
\][/tex]
Therefore, the cost for 45 kWh of electricity is R 35.94, confirming the provided statement.
---
### 1.1.2 Calculate the cost of Marisel's electricity if she uses 240 kWh of electricity during a particular month.
To calculate Marisel’s cost for using 240 kWh in a month, we need to use the tiered pricing structure. Here’s the breakdown of how the total cost is calculated, step-by-step:
1. For the first 50 kWh, the cost is:
[tex]\[
50 \times 0.7986 = 39.93
\][/tex]
2. For the next 190 kWh (from 51 kWh to 240 kWh), the cost is:
[tex]\[
190 \times 1.0755 = 204.345
\][/tex]
3. The total cost for 240 kWh is the sum of the costs for each tier:
[tex]\[
39.93 + 204.345 = 244.275
\][/tex]
Therefore, the total cost for Marisel's electricity usage of 240 kWh is R 244.275.
After rounding to two decimal places, the cost is:
[tex]\[
244.28
\][/tex]
So, the final cost for Marisel's electricity usage of 240 kWh for the month is approximately R 244.28.
