SOLUTION: on a trip jennifer noticed that her car averaged 21 mi/gal of gas except for the days she used the air conditioning, and then it averaged only 17 mi/gal. if she use 91 gal of gas t

Let x be the miles where she used the air conditioning.

Then miles where she didn't use the air conditioning were (1751-x).


Now we can write this equation for the total gas spent

     +  = 91 gallons of gas (total).    (*)


    +------------------------------------------------+
    |    At this point, the setup is just complete,  |
    |    and our task is to solve this equation.     |
    +------------------------------------------------+


For it, multiply both sides by 21*17.  You will get

    17x + 21*(1751-x) = 91*21*17

    17x + 21*1751 - 21x = 32487

    17x - 21x = 32487 - 21*1751

       -4x    =    -4284

         x    =     = 1071.


ANSWER.  She used the air conditioning on 1071 miles.


CHECK.  I will check if equation (*) is held.

         +  = 51 + 40 = 91 gallon of gas, in total.   ! Correct !