Question

A family has two cars. During one particular week, the first car consumed 20 gallons of gas and the second consumed 25 gallons of gas. The two cars drove a combined total of 800 miles, and the sum of their fuel efficiencies was 35 miles per gallon. What were the fuel efficiencies of each of the cars that week?

Answer 1

The car using 20 gallons got 15 miles per gallon.

The car using 25 gallons got 20 miles per gallon.

Explanation:

Let x and y represent the "miles per gallon" of the cars using 20 gallons and 25 gallons, respectively.

... 20x +25y = 800 . . . . . total miles traveled

... x + y = 35 . . . . . . . . . . sum of gas mileage numbers

Subtracting 20 times the second equation from the first gives ...

... (20x +25y) -20(x +y) = (800) -20(35)

... 5y = 100

... y = 20

... x = 35 -y = 15

The cars using 20 and 25 gallons got 15 and 20 miles per gallon, respectively.