Solving system of inequalities with a word problem.

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
1575
miles, for a total gas consumption of
55
gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

x=# of gallons used by the 25mpg car

y=# of gallons used by the 30 mpg car

x+y=55

25x+30y=1575

x=55-y

substitute

25(55-y)+30y=1575

1375-25y+30y=1575

1375+5y=1575

5y=1575-1375

5y=200

y=200/5

y=40 gallons

x+40=55

x=15 gallons