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The graph shows the cost of electricity with Company A - OCR - GCSE Maths - Question 3 - 2020 - Paper 6
Question 3
The graph shows the cost of electricity with Company A. (a) Use the information in the graph to estimate the cost of electricity for a customer who uses 450 kWh of ... show full transcript
Worked Solution & Example Answer:The graph shows the cost of electricity with Company A - OCR - GCSE Maths - Question 3 - 2020 - Paper 6
Step 1
Use the information in the graph to estimate the cost of electricity for a customer who uses 450 kWh of electricity.
Answer
To estimate the cost of electricity for a usage of 450 kWh, locate the corresponding point on the graph for 450 kWh. As the line representing the cost is linear, you can use the slope to calculate it. Assuming the line increases steadily, interpolate between noted points on the graph.
From the graph, if 0 kWh costs £0 and 250 kWh costs approximately £30, we can determine the cost per kWh is about £0.12.
Cost calculation:
[ \text{Cost} = 450 \text{ kWh} \times \text{Cost per kWh} = 450 \times 0.12 = £54.00 ]
Thus, the estimated cost of electricity for 450 kWh is approximately £54.00.
Step 2
If Company B's cost of electricity was plotted on the same axes as Company A's cost of electricity, which line would be steeper? Explain how you know.
Answer
Company B would have the steeper line because it charges 14.3 pence per kWh, which translates to £0.143 per kWh.
To compare the slopes, we can see that:
- For Company A's cost (approx. £0.12 per kWh), the line rises more gradually.
- For Company B, the steeper rise indicates a higher cost increase per unit, resulting in a steeper line on the graph.
Therefore, Company B's cost increases more rapidly with additional electricity usage.