Let \( x \) be the number of hours Naomi worked tutoring. Since she worked 2 more hours washing cars than tutoring, the number of hours she worked washing cars can be expressed as \( x + 2 \).
Next, we will set up the equation based on the total earnings. Her earnings from tutoring, at $12 per hour, would be:
\[ 12x \]
Her earnings from washing cars, at $10 per hour, would be:
\[ 10(x + 2) \]
The total earnings last week is given as $108. Therefore, we can set up the following equation:
\[ 12x + 10(x + 2) = 108 \]
Now, simplify the equation:
\[ 12x + 10x + 20 = 108 \]
Combine like terms:
\[ 22x + 20 = 108 \]
Next, subtract 20 from both sides:
\[ 22x = 88 \]
Now, divide both sides by 22:
\[ x = 4 \]
So, Naomi worked 4 hours tutoring. To find the number of hours she worked washing cars, we calculate:
\[ x + 2 = 4 + 2 = 6 \]
Thus, Naomi worked 6 hours washing cars and 4 hours tutoring last week.
To confirm, we can check the total earnings:
- Earnings from tutoring: \( 12 \times 4 = 48 \)
- Earnings from washing cars: \( 10 \times 6 = 60 \)
Adding these together:
\[ 48 + 60 = 108 \]
The calculations are consistent with the given total. Therefore, the final answer is:
- Washing Cars: 6 hours
- Tutoring: 4 hours
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