A family has two cars. The first car has a fuel efficiency of 

12

 kilometers per liter of gas and the second has a fuel efficiency of 

16

 kilometers per liter of gas. During one particular week, the two cars went a combined total of 

3620

 kilometers, for a total gas consumption of 

250

 liters. How many liters were consumed by each of the two cars that week?

To solve the problem, we can use a system of linear equations. Let's denote the number of liters consumed by the first car as \( x \) and the number of liters consumed by the second car as \( y \).

### Step 1: Write down the equations based on the problem

1. **Equation for total kilometers driven:**
   - The first car has a fuel efficiency of 12 km/L, so it drives \( 12x \) kilometers on \( x \) liters.
   - The second car has a fuel efficiency of 16 km/L, so it drives \( 16y \) kilometers on \( y \) liters.
   - The combined total distance driven by both cars is 3620 kilometers. Therefore, the equation is:
   \[
   12x + 16y = 3620
   \]

2. **Equation for total gas consumption:**
   - The total gas consumed by both cars is 250 liters. Therefore, the equation is:
   \[
   x + y = 250
   \]

### Step 2: Solve the system of equations

First, solve the second equation for one variable (let's solve for \( x \)):
\[
x = 250 - y
\]

Now, substitute this expression for \( x \) into the first equation:
\[
12(250 - y) + 16y = 3620
\]

Expand and simplify:
\[
3000 - 12y + 16y = 3620
\]
\[
4y = 3620 - 3000
\]
\[
4y = 620
\]
\[
y = 155
\]

Now that we have \( y = 155 \), we can find \( x \) using the equation \( x + y = 250 \):
\[
x = 250 - 155 = 95
\]

### Step 3: Interpret the solution

The first car consumed **95 liters**, and the second car consumed **155 liters**.

### Summary:
- **First car:** 95 liters
- **Second car:** 155 liters

Would you like more details or have any questions?

### Additional Questions:
1. Would you like to see the solution process using a different method, like substitution or elimination?
2. Do you need help verifying the solution by plugging the values back into the original equations?
3. Are you interested in learning how to solve similar problems involving systems of equations?
4. Would you like to explore the concept of fuel efficiency and how it relates to the distance traveled?
5. Do you want to understand the geometric interpretation of the solution on a graph?
6. Are you curious about how small changes in fuel efficiency or distance could affect the total gas consumption?
7. Would you like an example of a similar problem with different numbers?
8. Do you need a brief review of how to set up and solve linear equations?

### Tip:
When dealing with word problems, clearly defining variables and translating the problem into mathematical equations is key to finding the correct solution.

Learn how to calculate gas consumption using systems of linear equations with a detailed step-by-step solution. This problem involves two cars with different fuel efficiencies and total distance traveled. Suitable for high school students.

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