Solving a value mixture problem using a system of linear equations
Ryan
A family 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 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 1500 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week?
First car: Øٓ gallons
Second car: $\square$ gallons

Step 1 ：Let's denote the number of gallons consumed by the first car as \(x\) and the number of gallons consumed by the second car as \(y\).

Step 2 ：We can set up the following two equations based on the problem: \(25x + 40y = 1500\) (This equation represents the total distance travelled by the two cars) and \(x + y = 45\) (This equation represents the total gas consumption of the two cars).

Step 3 ：Solving this system of equations, we find that \(x = 20\) and \(y = 25\).

Step 4 ：This means that the first car consumed 20 gallons of gas and the second car consumed 25 gallons of gas during that week.

Step 5 ：Final Answer: The first car consumed \(\boxed{20}\) gallons and the second car consumed \(\boxed{25}\) gallons.