Calculating the Cost of Electricity (WJEC GCSE Science (Double Award): Physics): Revision Note

In the month of January, a 3 bedroom household used 284 kWh of electricity, and 1366 kWh of gas.

The household's tariff details are listed below.

• Electricity unit price: 26.47 p/kWh

• Electricity standing charge: 51.38 p/day

• Gas unit price: 7.00 p/kWh

• Gas standing charge: 26.16 p/day

Calculate the total price of the energy bill for the month of January.

The month of January has 31 days. Ignore the cost of VAT tax. 

Answer:

Step 1: List the known quantities

• Electricity used = 284 kWh

• Electricity unit price = 26.47 p/kWh

• Gas used = 1366 kWh

• Gas unit price = 7.00 p/kWh

• Electricity standing charge = 51.38 p/day

• Gas standing charge = 26.16 p/day

Step 2: Write out the equation for calculating the cost of energy

Cost = units used × cost per unit

Step 3: Calculate the cost of the electricity used

$\mathrm{cost}\mathrm{of}\mathrm{electricity}=284\times 26.47$

$\mathrm{cost}\mathrm{of}\mathrm{electricity}=7517.48\mathrm{p}$

• Convert pence (p) to pounds (£) by dividing by 100 and rounding to the nearest pence

$\mathrm{cost}\mathrm{of}\mathrm{electricity}=\frac{7517.48}{100}=\pounds 75.17$

Step 4: Calculate the cost of the gas used

$\mathrm{cost}\mathrm{of}\mathrm{gas}=1366\times 7.00$

$\mathrm{cost}\mathrm{of}\mathrm{gas}=9562\mathrm{p}$

$\mathrm{cost}\mathrm{of}\mathrm{gas}=\frac{9562}{100}=\pounds 95.62$

Step 5: Calculate the total standing charge for electricity

total standing charge electricity = standing charge per day × number of days

$\mathrm{total}\mathrm{standing}\mathrm{charge}\mathrm{electricity}=51.38\times 31$

$\mathrm{total}\mathrm{standing}\mathrm{charge}\mathrm{electricity}=1592.78\mathrm{p}$

$\mathrm{total}\mathrm{standing}\mathrm{charge}\mathrm{electricity}=\frac{1592.78}{100}=\pounds 15.93$

Step 6: Calculate the total standing charge for gas

$\mathrm{total}\mathrm{standing}\mathrm{charge}\mathrm{gas}=26.16\times 31$

$\mathrm{total}\mathrm{standing}\mathrm{charge}\mathrm{gas}=810.96\mathrm{p}$

$\mathrm{total}\mathrm{standing}\mathrm{charge}gas=\frac{810.96}{100}=\pounds 8.11$

Step 7: Add all the individual costs together to find the total cost of the bill

Total cost of bill = cost of electricity + cost of gas + total standing charge electricity + total standing charge gas

$\mathrm{total}\mathrm{cost}=\pounds 75.17+\pounds 95.62+\pounds 15.93+\pounds 8.11$

$\mathrm{total}\mathrm{cost}=\pounds 195.47$

The price per unit is given in pence (p), but the total amounts are billed in pounds (£). Unless the exam question tells you otherwise, you should convert your answer into pounds and round to the nearest pence.