Afamily 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?

The car using 20 gallons got 15 miles per gallon.

The car using 25 gallons got 20 miles per gallon.

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.

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