A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas.

Question

A family has two cars. The first car has a fuel efficiency of
20
miles per gallon of gas and the second has a fuel efficiency of
40
miles per gallon of gas. During one particular week, the two cars went a combined total of
1700
miles, for a total gas consumption of
50
gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

It is extremely important to consider units in this type of problem.  Fuel efficiency is given in miles/gal, so:

     miles = (miles/gallon)*(gallons)                [gallons cancel]

 

Let x = gallons consumed by car1

     y = gallons consumed by car2

 

Translate:

  "combined total of 1700 miles"     means

  (miles for car1) + (miles for car2) = 1700              [eq1]

 

  "total gas consumption of 50 gallons"      means

   (gas consumed by car1) + (gas consumed by car2) = 50         means

                x                     +                 y                  = 50           [eq2]

 

The math:

   Use eq2 to solve for one of the variables (say, x):     x = 50-y      [eq3]

 

   Substitute into the other equation (that is, eq1):

       (miles for car1) + (miles for car2) = 1700              [eq1 again]

 

        (20 miles/gal)(x gal)  +  (40 miles/gal)(y gal)  =  1700 miles            [use given fuel efficiency)

             20x + 40y = 1700

             20(50-y) + 40y = 1700                    [use eq3 to substitute for x]

             1000 - 20y + 40y = 1700 

                   20y = 700

                     y = 35

The second car used 35 gallons.

 

Now, use either eq3 to find x:

       x = 50-y

       x = 50-35

       x = 15

The first car used 15 gallons.

 

Check:

  Is   35 + 15 = 50   ?

           50 = 50   ?yes

  Is   20(15) + 40(35) = 1700   ?

          300 + 1400 = 1700   ?

             1700 = 1700   ?yes