Discrete Mathematics

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There are two plans for renting a car. Plan A charges $10 per day plus a $50 one-time fee. Plan B charges $15 per day plus a $30 one-time fee. How many days must you rent the car for Plan A to be a better deal than Plan B?

  • Discrete Mathematics -

    we need

    50+10d < 30+15d

    so, ...

  • Discrete Mathematics -

    50 + 10d < 30 + 15d
    -10d < - 10d
    50 < 30 + 5d
    -30 -30
    20 < 5d
    /5 < 5
    4 < d

    Please tell me if this is the right answer.

  • Discrete Mathematics -

    Looks good to me.
    If more than 4 days of rental, A is the better deal.

    At d=4, A=B=90
    After that, A grows more slowly than B.

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