Afamily has two cars. the first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. during one particular week, the two cars went a combined total of 1525 miles, for a total gas consumption of 40 gallons. how many gallons were consumed by each of the two cars that week?

Let x and y represent the numbers of gallons used by the 40 mpg and 35 mpg cars, respectively.
.. x +y = 40 . . . . . . . . . . .total consumption is 40 gallons
.. 40x +35y = 1525 . . . . total miles driven = 1525

Multiply the first equation by 40 and subtract the second.
.. 40(x +y) -(40x +35y) = 40(40) -(1525)
.. 5y = 75
.. y = 15
.. x = 40 -15 = 25

The 40 mpg car consumed 25 gallons.
The 35 mpg car consumed 15 gallons.