Question

Mercy's family used 690 kWh in January 2022 and paid R596,11 using option 1. Mercy told the father that had they chosen a pre-paid option 2, they would have paid R163,38 more. Use the calculations to verify if Mercy was correct.​

Answer 1

Explanation:

Let's first calculate the cost per kilowatt-hour (kWh) for option 1.

Cost per kWh = Total cost / Total kWh used

Cost per kWh = R596.11 / 690 kWh

Cost per kWh = R0.8637/kWh

Now, let's assume that for option 2, the cost per kWh is higher by an amount of x. Then the cost per kWh for option 2 would be:

Cost per kWh for option 2 = Cost per kWh for option 1 + x

We know that the total cost for option 2 is R163.38 more than option 1. So, we can set up an equation based on this:

Total cost for option 2 - Total cost for option 1 = R163.38

Cost per kWh for option 2 x Total kWh used - Cost per kWh for option 1 x Total kWh used = R163.38

(x + R0.8637/kWh) x 690 kWh - R0.8637/kWh x 690 kWh = R163.38

Simplifying:

690x + R596.11 - R596.11 = R163.38

690x = R163.38

x = R163.38 / 690

x = R0.237

So, the cost per kWh for option 2 is R0.8637/kWh + R0.237/kWh = R1.1007/kWh

Now, let's calculate the total cost for option 2:

Total cost for option 2 = Cost per kWh for option 2 x Total kWh used

Total cost for option 2 = R1.1007/kWh x 690 kWh

Total cost for option 2 = R759.28

So, according to the calculations, the total cost for option 2 would be R759.28, which is R163.17 more than the cost of option 1. Therefore, Mercy was incorrect in stating that the cost for option 2 would be R163.38 more than option 1. The actual difference is R163.17.