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  • Perplex
    IB Math AISL
    /
    Modelling
    /

    Problem Bank

    [Maximum mark: 4]

    At a car rental company ​A, the following prices are offered for a ​1​ day rental.

    • Pickup & cleaning cost: ​$45​

    • Gas and depreciation: ​$0.7​ per mile driven

    1. Write down an expression for ​A(x), the cost of a rental driven ​x​ miles.

      [1]

      To earn a crown, get your answer ready before you reveal the options!

    A customer rents a car from company ​A​ and drives it ​80​ miles in a day.

    1. Calculate the cost of the rental to the nearest dollar.

      [1]

    A competitor, company ​B, offers the following prices for a ​1​ day rental.

    • Pickup & cleaning cost: ​$65​

    • Gas and depreciation: ​$0.48​ per mile driven

    1. Find the minimum distance a customer must drive (to the nearest mile) for company ​B​ to become a cheaper option than company ​A.

      [2]

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