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The question in the image reads:

**Savings Application:**
Perry has $120 in savings and is planning to add $40 each week. Sofia has $400 in savings and is planning to add $30 each week. Their plan is to wait until their savings are equal and then load up their old Volkswagen bus and take a road trip. They figure out that the equation used to determine how many weeks it will take until their savings are equal is:

\[ 40w + 120 = 30w + 400 \]

Where $ w $ is the number of weeks they have been saving.

The question asks:
- How many weeks will Perry and Sofia have to continue to save until they both have the same amount in savings and they can go on their road trip?

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We can solve this linear equation to find $ w $, the number of weeks.

1. Start with the equation:
   \[
   40w + 120 = 30w + 400
   \]

2. Subtract $ 30w $ from both sides to get:
   \[
   40w - 30w + 120 = 400
   \]
   \[
   10w + 120 = 400
   \]

3. Subtract 120 from both sides:
   \[
   10w = 400 - 120
   \]
   \[
   10w = 280
   \]

4. Divide both sides by 10 to find $ w $:
   \[
   w = \frac{280}{10} = 28
   \]

So, it will take **28 weeks** for Perry and Sofia to have the same amount of savings.

Would you like a more detailed explanation, or do you have any other questions?

---

Here are 5 related questions to explore further:

1. What would happen if Perry increased his weekly savings by $10?
2. How would the equation change if Sofia started with $500 instead of $400?
3. Can you generalize an equation for any initial savings and weekly contribution?
4. What if Sofia decided to save $50 a week instead of $30? How many weeks would it take then?
5. What would be the impact if Perry spent $100 from his savings before they started saving weekly?

**Tip**: When solving linear equations, always simplify step by step, combining like terms first to avoid confusion.

Perry has $120 in savings and is planning to add $40 each week. Sofia has $400 in savings and is planning to add $30 each week. Their plan is to wait until their savings are equal and then load up their old Volkswagen bus and take a road trip. The equation used to determine how many weeks it will take until their savings are equal is 40w + 120 = 30w + 400. How many weeks will Perry and Sofia have to save until they both have the same amount in savings?

Learn how to solve the linear equation 40w + 120 = 30w + 400 to find out how many weeks Perry and Sofia need to save to have the same amount. This example covers core algebraic concepts, including solving for variables in linear equations. Suitable for students in Grades 7-9.

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