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 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1325 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of
the two cars that week?

Step-by-step explanation:

Assume that the mile-per-gallon car consumed all that gallons of fuel. How far would the cars have travelled?

.

This assumption overestimated the total mileage of the two cars by . Here's why: for every gallon that the second ( mile-per-gallon) car consumed, this assumption would overestimate the total mileage by . Therefore, the overestimation of corresponds to:

.

Therefore, the second car consumed . The first car would have consumed .

Verify the results: .