Question

A family has two cars. The first car has a fuel efficiency of 35 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 1375 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of

the two cars that week?

Answer 1

Explanation:

Let's call the number of gallons of gas consumed by the first car "x" and the number of gallons of gas consumed by the second car "y". We can set up a system of two equations to represent the information given in the problem:

x + y = 45 (equation 1: total gas consumption is 45 gallons)

35x + 25y = 1375 (equation 2: total distance traveled is 1375 miles)

To solve for x and y, we can use the first equation to solve for one variable in terms of the other. For example, we can solve for y as:

y = 45 - x

We can then substitute this expression for y into the second equation, and simplify:

35x + 25(45 - x) = 1375

35x + 1125 - 25x = 1375

10x = 250

x = 25

So the first car consumed 25 gallons of gas that week. We can substitute this value into equation 1 to find the number of gallons consumed by the second car:

25 + y = 45

y = 20

Therefore, the second car consumed 20 gallons of gas that week.