Linear equations

Question

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 25 miles per gallon of gas. During one particular week, the two cars went a combined total of 1425 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

X + Y = 65, Y=65-X

1425 = 25X + 20(65-X) = 25X + 1300 -20X = 1300+5X

5X = 1425-1300 = 125

X = 125/5 = 25 gallons for the 2nd car with 25 mpg

Y= 65-25 = 40 gallons for the 1st car with 20 mpg

1st car went 40x20 = 800 miles

2nd car went 25x25 = 625 miles

total miles = 800+625 = 1425