Let's denote the number of weeks Chelsea has been paying her mom back as \( w \).
Initially, Chelsea owes her mom $38. She pays back $4 for each week, so after \( w \) weeks, the total amount she has paid back is \( 4w \).
The amount she owes after paying back for \( w \) weeks can be represented as:
\[ 38 - 4w \]
According to the problem, after some weeks, she realizes she owes her mom $2 more. This means:
\[ 38 - 4w = 2 \]
Now, we will solve this equation for \( w \).
- Start by isolating the term with \( w \):
\[ 38 - 4w = 2 \]
- Subtract 38 from both sides:
\[ -4w = 2 - 38 \] \[ -4w = -36 \]
- Now, divide both sides by -4:
\[ w = \frac{-36}{-4} = 9 \]
Thus, Chelsea has been paying her mom back for 9 weeks.
To verify:
- Total amount owed originally: $38
- Amount paid back in 9 weeks: \( 4 \times 9 = 36 \)
- Amount owed after 9 weeks: \( 38 - 36 = 2 \)
The calculations check out, confirming that Chelsea has been paying her mom back for 9 weeks.