Question

Solve the equation that can be used to solve. Chelsea owes her mom $38. She starts paying her mom back $4 per week. After some weeks, she realized she only owes her mom $2 more. How many weeks has she been paying her mom back?

Answer 1

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 \( w \).

1. Start by isolating the term with \( w \):

\[
38 - 4w = 2
\]

2. Subtract 38 from both sides:

\[
-4w = 2 - 38
\]
\[
-4w = -36
\]

3. 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**.