linear equatations

Question

A family has two cars. The first car has a fuel efficiency of 40 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 1875 miles, for a total gas consumption of 60 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Hi James,

Let x = the gallons consumed by the first car.

Let y = the gallons consumed by the second car.

We are told that:

40x + 25y = 1875

x + y = 60

If we multiply the second equation by -25, we get:

40x + 25y = 1875

-25x - 25y = -1500

If we add these two equations together;

15x = 375

x = 25 gallons.

Since we know x + y = 60, then 25 + y = 60 so y = 35 gallons.

Please let me know if I can be more helpful, thanks!

Joe