Solving a value mixture problem using a system of linear equations

Question

A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 30 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 60 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

25F + 30S = 1700

F+S = 60

25F + 25S = 1500

5S =200

S =40 gallons for the second car that gets 30 mpg

F=20 gallons for the first care that gets 25 mpg

20(25) + 40(30) = 500+1200=1700