Question

A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. During one particular week, the two cars went a combined total of 1275 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

The first car consumed 15 gallons and the second car consumed 30 gallons.

Step-by-step explanation:

In order to find out how many gallons were consumed by each of the two cars, we can set up a system of equations.

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 can write the following equations based on the given information:

1. x + y = 45 (the total gas consumption)
2. 15x + 35y = 1275 (the total distance traveled)

To solve this system of equations, we can use the substitution method. Solving equation 1 for x, we get x = 45 - y. Substituting this into equation 2, we have 15(45 - y) + 35y = 1275. Simplifying this equation, we get 675 - 15y + 35y = 1275. Combining like terms, we have 20y = 600. Dividing both sides by 20, we get y = 30. Substituting this value of y back into equation 1, we get x = 45 - 30 = 15.

Therefore, the first car consumed 15 gallons and the second car consumed 30 gallons.