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Rent a Van An Investigation

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Rent a Van A man wants to hire a caravanette for one week for his family holiday. Two local firms offer him the following rates :- Firm A : £65 per week plus 4p per mile Firm B : £55 per week plus 6p per mile a)Make a table to show the costs of hiring from the two firms as shown below Mileage100200400600800 Firm A Firm B b)On the same set of axes, draw line graphs of Cost against Mileage (i.e. Mileage axis across the page and Cost axis up the page) for each firm. Note:- It is not necessary to start the Cost axis at zero. c)Which firm should the man choose?

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2.A lady is moving house and decides to hire a van. Here are three different hire rates she has been quoted:- X Fixed price of £45 per day Y £20 per day plus 6p per mile Z £14 per day plus 8p per mile a)Make up a table showing the costs of hiring a van using each scheme for mileages up to 500 miles. b)Draw line graphs, on the same set of axes, of Cost against Mileage for all three schemes. c)From the graphs, write down the mileages for which each scheme is best. d)If C is the cost in £ for a distance of M miles, write down a formula for C in terms of M for scheme Y and scheme Z. e)Verify that the formulae give the same value for C when M = 300. f)Use the formula for scheme Y and the cost for scheme X to find out at what exact mileage schemes X and Y have the same cost.

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Solutions

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Solution 1. a)Mileage100200400600800 Firm A£69£73£81£89£97 Firm B£61£67£79£91£103 Firm B for less than 500 miles, otherwise Firm A.

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2.Mileage100200300400500 X£45£45£45£45£45 Y£26£32£38£44£50 Z£22£30£38£46£54

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c) Scheme Distance Zless than 300 miles Y300 to 416 miles Xover 416 miles d) (Y)C = 20 + 0·06 × M (Z)C = 14 + 0·08 × M e)20 + 0·06 × 300 = 20 + 18 = 38 14 + 0·08 × 300 = 14 + 24 = 38 f)20 + 0·06 × M = 45 0·06 × M = 25 M = 25 ÷ 0·06 = 416

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