Afamily 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 15 miles per gallon of gas. during one particular week, the two cars went a combined total of 1375 miles, for a total gas consumption of 65 gallons. how many gallons were consumed by each of the two cars that week?

The answer is:

First car:  40 gallons consumed

Second car: 25 gallons consumed

We can solve this problem by using a 2 x 2 system of equations. Let's pose the equations that will help us to determinate what we need to know.

Y = gallons consumed by the first car

Z = gallons consumed by the second car

We know from the statement that both cars combine a 1375 miles travel.

So, for the 1st equation we have

We also know that both cars consume a total of 65 gallons.

So, for the 2nd equation we have

By substituting the 2nd equation in the 1st equation, we have

So, we have that the first car consumption is 40 gallons.

To know the second car consumption, we just need to substitute Y in the 2nd equation,

By substituting, we have

The second car consuption is 25 gallons.

Have a nice day!