SOLUTION: A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one pa

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Question 1143760: A family has two cars. The first car has a fuel efficiency of
35
miles per gallon of gas and the second has a fuel efficiency of
15
miles per gallon of gas. During one particular week, the two cars went a combined total of
825
miles, for a total gas consumption of
35
gallons. How many gallons were consumed by each of the two cars that week?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!



VEHICLE       FUEL EFFIC.    VOLUME      DISTANCE(miles)

FirstCar        35            v           35v

SecondCar       15            35-v       15(35-v)

TOTALS                        35         825


.
.
-------gallons fuel, the firstcar
------gallons fuel, the secondcar
Answer by ikleyn(52884)   (Show Source): You can put this solution on YOUR website!
.

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.


ANSWER.  First car consumed 15 gallons of gas; second car consumed the rest  35-15 = 20 gallons of gas.

Solved.



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