A family has two cars. The first car has a fuel efficiency of

Question

A family has two cars. The first car has a fuel efficiency of 30

miles per gallon of gas and the second has a fuel efficiency of 40

miles per gallon of gas. During one particular week, the two cars went a combined total of 2050

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=# gallons used by the 30 mpg car

y=# gallons used by the 40 mpg car

30x+40y=2050

x+y=55

simplify the first equation

3x+4y=205

x+y=55

x=55-y

substitute

3(55-y)+4y=205

165-3y+4y=205

165+y=205

y=205-165

y=40 gallons

x+40=55

x=55-40

x=15 gallons