Question 1143760
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Let x = fuel amount (in gallons) consumed by the first car at 35 mi/gallon, and 

let y = fuel amount (in gallons) consumed by the second car at 15 mi/gallon.


From the condition, you have these two equation


      x +   y =  35  gallons    (1)

    35x + 15y = 825  miles      (2)


Simplify by dividing equation (2) by 5 (both sides). You will get


      x +   y =  35             (3)

     7x +  3y = 165             (4)


From equation (3), express  y = 35-x  and substitute it into equation (4).  You will get


     7x + 3*(35-x) = 165

     7x + 105 - 3x = 165

     7x - 3x       = 165 - 105

     4x            = 60

      x            = 60/4 = 15.


<U>ANSWER</U>.  First car consumed 15 gallons of gas; second car consumed the rest  35-15 = 20 gallons of gas.
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Solved.