Story problem--

Question

John rented a car from a company that charged a daily rental fee along with charge per mileage. He rented a car for 5 days and drove 300 miles and was charged $330. His friend Amanda later rented the same car for 8 days drove 280 miles and was charged $458. What was the daily rental charge? What was the Charge per mile?

Answer 1

The daily rental fee is in units of $.  The charge per mile is in units of ($/mi).  When we multiply the charge per mile by the number of miles driven, that is ($/mi)(mi), the miles cancel out, leaving only the $.

 

Let:

    F = the daily rental fee

    P = the per mile fee

This is "the same car," so F and P are constant.

 

John paid:           $330 = 5F + (P)300              [eq1]

Amanda paid:      $458 = 8F + (P)(280)           [eq2]

 

Now, use either substitution or elimination or find the values of F and P.  Let's use elimination.

John paid:           528 = 8F + 480p         [eq1 times 8/5]

Amanda paid:      458 = 8F + 280p         [eq2]

                        --------------------

                            70 =        200p     (elimination method; subtract equations)

                           0.35 = p               (divide both sides by 200)

 

   330 = 5F + (70/200)300            Substitute value for p into eq1

   330 = 5F +  105                 

      225 = 5F                    (subtract 105 from both sides)

         45 = F                     (divide both sides by 5)

 

Checking (very important):

  Is  (5)(45) + (0.35)(300) = 330  ?

        225  +  105 = 330   ?

            330 = 330   ? yes

  Is (8)(45) + (0.35)(280) = 458   ?

          360 + 98 = 458   ?

              458 = 458   ? yes