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 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 2200 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?

The car that has a fuel efficiency of 40 mpg consumed 35 gallons, while the car that has a fuel efficiency of 20 mpg consumed 40 gallons.

Step-by-step explanation:

The variable a will represent the fuel consumed by the first car, and the variable b will represent the fuel consumed by the second car.

Set up the formula: a+b=75, which will represent the total gas consumption.

The formula 20a+40b=2200 will help you solve.

To solve, we will first solve for a by changing the formula from a+b=75 to b=75-a. Then you plug in the value of b to the second formula:

20a+40(75-a)=2200

20a+3000-40a=2200

3000-20a=2200

After subtracting 3000 from both sides, you are left with -20a=-800. Multiply both sides by -1 so that both sides are positive:

20a=800

a=40

Now that we know that the car with a 20 mpg fuel efficiency consumed 40 gallons that week, we can subtract 40 from 75, leaving us with 35 being the amount of gallons consumed by the car with a 40 mpg efficiency.