Utilities are services such as gas, electricity, water and telephones. A a utility may have a standing charge - a fixed amount - plus an amount which depends on how much of the supply has been used.

For power and water, the variable amount is worked out from meter readings. The meters are attached to the house, and the amount used is calculated by subtracting the previous meter reading from the current reading. Meter readings are used to work out the amount of energy used in kilowatt-hours (kWh).

At the start of last month, Jack had an electric meter reading of 5066. At the end of the month, the meter reading is 5545. If the cost of electricity is 15.4p for each unit and VAT is at 5% for energy, how much did the electricity cost him lost month?

There is no standing charge for Jack.

Electricity used = 5545 - 5066 = 479 units

Cost = 479 x 15.4 = 7376.6p

VAT multiplier = 1 + `frac(5)(100)` = 1.05

Final cost = 7376.6 x 1.05 = 7745.43p, or £77.45

Answer: £77.45

The cost of gas is changing from 136.22p to 134.5p per kWh. Emily has used 142 kWh at the higher rate, and 86 kWh at the lower rate. The standing charge is 15.45 over the billing period, and the VAT rate to be applied is 5%. What is the final bill for Emily for her gas?

Calculate the costs for the two separate rates

Gas cost = 136.22 x 142 + 134.5 x 86 = 19343p + 11567p = 30910p

Add in the Standing Charge = 30910p + 1545p = 32455p

VAT multiplier = 1 + `frac(5)(100)` = 1.05

Total cost = 32455p x 1.05 = 34077.75p, or £340.78.

Answer: £340.78

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