Next week you have to travel around parts of the country on business and have decided to hire a car from a car-hire company. You have contacted two companies which offer different services. The first company will rent you a car for £45 per day.

The second company will charge you £30 per day but with an additional charge of 5p per mile travelled. You know you will require the car for four days but are unsure of the mileage you will cover.

(a) Determine mathematically what mileage you would need to cover to make the second company’s charge cheaper.

(b) Confirm this using graphs.

(c) Both companies now realise that they will need to add VAT at 20 per cent to the charge for the daily hire but not to the charge for the mileage covered. How will this affect your decision?