Naomi is working two summer jobs, making $10 per hour washing cars and $12 per hour tutoring. Last week Naomi earned a total of $108 and worked 2 more hours washing cars than hours tutoring. Determine the number of hours Naomi worked washing cars last week and the number of hours she worked tutoring last week.

Let's define the variables:
- Let $ x $ represent the number of hours Naomi worked tutoring.
- Let $ x + 2 $ represent the number of hours Naomi worked washing cars, since she worked 2 more hours washing cars than tutoring.

Now, we'll calculate Naomi's total earnings:
- Naomi earns $12 per hour tutoring, so her earnings from tutoring are $ 12x $.
- Naomi earns $10 per hour washing cars, so her earnings from washing cars are $ 10(x + 2) $.

According to the problem, Naomi earned a total of $108 last week. Therefore, the equation is:

\[
12x + 10(x + 2) = 108
\]

### Step 1: Expand the equation
\[
12x + 10x + 20 = 108
\]

### Step 2: Combine like terms
\[
22x + 20 = 108
\]

### Step 3: Subtract 20 from both sides
\[
22x = 88
\]

### Step 4: Solve for $ x $
\[
x = \frac{88}{22} = 4
\]

Thus, Naomi worked $ 4 $ hours tutoring.

### Step 5: Calculate the hours washing cars
\[
x + 2 = 4 + 2 = 6
\]

Naomi worked 6 hours washing cars.

### Conclusion:
- Naomi worked **6 hours washing cars** and **4 hours tutoring** last week.

Would you like any additional details or explanations? 

Here are 5 related questions to explore further:
1. What if Naomi worked 3 more hours washing cars than tutoring? How would the solution change?
2. How much would Naomi earn if she worked 5 hours tutoring and 7 hours washing cars?
3. If Naomi earned $150 next week with the same rate, how many total hours would she have worked?
4. How would the equation change if Naomi worked fewer hours washing cars than tutoring?
5. What would happen if the pay rate for washing cars increased to $15 per hour?

**Tip:** When solving word problems, defining variables based on the problem's relationships helps to set up accurate equations.

Solve the problem of determining how many hours Naomi worked at two jobs by using algebraic equations. This problem involves calculating total earnings and using linear equations, suitable for students in Grades 6-8.

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