I need help I'am killing my head with maths!!!!!!please somebody help me?

Question

Hello

Please I really tried to find a solution but I am not good at maths!!! Thank you for anyone who can help me. Here are the exercises:

Electricity cost 10.36p per unit day-time or 4.67 per unit night time but to qualify for the night time rate customers need to pay an extra £10.49 a quarter (13 weeks) for a special meter.

How many units (to the nearest whole unit) on average per week would a customer need to use at night time to break even on the extra cost?

If a customer made an overall saving of £20 over the quarter how many units (to the nearest one) would he have used at the night time rate?

If a customer used a total of 125 night-time units over a quarter would this result in a loss or a saving and by how much (to the nearest p) allowing for the extra charge for the meter?

Thanks

Answer 1

Assuming 100p = £1
The difference in per-unit cost is
£0.1036 - £0.0467 = £0.0569/unit
The break-over usage is
£10.49 / (£0.0569/unit) = 184.3585 units in 13 weeks, or 184.3585/13 = 14.18142 units/week, or 15 units/week
(Note that 14 units/week does NOT break even)

For an overall savings of £20 over the quarter, the quaarterly usage would have to be
(£20 + £10.49) / (£0.0569/unit) =
(£30.49) / (£0.0569/unit) = 536 units

The savings / loss over a quarter for a usage of 125 night-time units is
£10.49 - (125 units)(£0.0569/unit) =
£10.49 - £7.11 = £3.38 loss, or 338p loss