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2 February, 23:29

George needs to rent a car for one day. He can rent a Cadillac from Gamma Car Rental for $30.39 per day plus 55 cents per mile. He can get the same car from Delta Car Rental for $50.31 per day plus 43 cents per mile. What number of miles results in the price for Gamma being equal to the price for Delta? Write your answer as a number only

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  1. 3 February, 00:52
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    Call the number of days 'd' and the number of miles 'm'.

    (Original, eh?)

    Then the equation for Gamma's price is

    Price-G = 30.39d + 0.55m

    and the equation for Delta's price is

    Price-D = 50.31d + 0.43m.

    We're going to set the prices equal, and find out

    what the number of miles is:

    Price-G = Price-D.

    30.39d + 0.55m = 50.31d + 0.43m.

    Before we go any farther, I'm going to assume that both cases would be

    one-day rentals. My reasons: = = > the solution for the number of miles

    depends on how many days each car was rented for; = = > even if both

    cars are rented for the same number of days, the solution for the number

    of miles depends on what that number of days is.

    For 1-day rentals, d=1, and

    30.39 + 0.55m = 50.31 + 0.43m.

    Beautiful. Here we go.

    Subtract 0.43m

    from each side: 30.39 + 0.12m = 50.31

    Subtract 30.39

    from each side: 0.12m = 19.92

    Divide each side by 0.12 : m = 166.

    There it is! If a car is rented from Gamma for a day, and another car

    is rented from Delta for a day, and both cars are driven 166 miles, then

    the rental prices for both cars will be the same ... (namely $121.69)
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