1. The George family used 250 kWh of electricity for the month of December. Calculate the amount they need to pay. 2. In January they used 351 kWh. Determine the difference between... 1. The George family used 250 kWh of electricity for the month of December. Calculate the amount they need to pay. 2. In January they used 351 kWh. Determine the difference between the December and January payments.
Understand the Problem
The question involves calculating electricity costs based on a tiered pricing structure. The first part requires calculating the total cost for a given consumption in December. The second part involves finding the difference in cost between December and January, where January's consumption is also provided. The key is to apply the correct rates for each kWh block according to the table.
Answer
1. 1 $R232.00$ 2. 2 $R98.16$
Answer for screen readers
- 1 The amount they need to pay in December is $R232.00$.
- 2 The difference between the December and January payments is $R98.16$.
Steps to Solve
- Calculate the cost for December
The George family used 250 kWh in December. We need to split this into the tiered blocks and calculate the cost for each block.
Block 1 (0-50 kWh): $50 \times R0.76 = R38.00$
Block 2 (51-250 kWh): This is $250 - 50 = 200$ kWh. $200 \times R0.97 = R194.00$
Total cost for December: $R38.00 + R194.00 = R232.00$
- Calculate the cost for January
In January, the George family used 351 kWh. We need to consider three blocks this time.
Block 1 (0-50 kWh): $50 \times R0.76 = R38.00$
Block 2 (51-350 kWh): This is $350 - 50 = 300$ kWh. $300 \times R0.97 = R291.00$
Block 3 (351 kWh): Since they used 351 kWh, only 1 kWh falls into this block. $1 \times R1.16 = R1.16$
Total cost for January: $R38.00 + R291.00 + R1.16 = R330.16$
- Calculate the difference between December and January payments
Difference = January cost - December cost
Difference = $R330.16 - R232.00 = R98.16$
- 1 The amount they need to pay in December is $R232.00$.
- 2 The difference between the December and January payments is $R98.16$.
More Information
The tiered pricing system is designed to encourage lower electricity consumption by charging higher rates for higher usage.
Tips
A common mistake is to not break the total kWh used into the correct blocks, and instead applying the wrong rate to the entire usage. It is also easy to make arithmetic errors when calculating.
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