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 2000 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of
the two cars that week?
Note that the ALEKS graphing calculator can be used to make computations easier.
First car: gallons
Second car: gallons
X
3

Answer 1

Answer: Let x be the number of gallons consumed by the first car and y be the number of gallons consumed by the second car.

We know that the total distance traveled is 2000 miles, and the total gas consumption is 55 gallons. We can set up two equations based on this information:

Equation 1: x + y = 55 (total gas consumption)

Equation 2: (30x/1) + (40y/1) = 2000 (total distance traveled)

Simplifying Equation 2, we get:

30x + 40y = 2000

Dividing both sides by 10, we get:

3x + 4y = 200

We can now use Equation 1 to solve for one of the variables in terms of the other. For example, we can solve for y:

y = 55 - x

Substituting this expression for y into Equation 2, we get:

3x + 4(55 - x) = 200

Simplifying and solving for x, we get:

x = 25

So the first car consumed 25 gallons of gas. Substituting this value into Equation 1, we can solve for y:

25 + y = 55

y = 30

So the second car consumed 30 gallons of gas.

Therefore, the first car consumed 25 gallons of gas and the second car consumed 30 gallons of gas.

Explanation: