https://file.aiquickdraw.com/mathbot/file/1726454726067mogqfooa.jpg

The problem presented in the image asks how many weeks Lian and Nia will have to continue saving until they both have the same amount of savings for their road trip.

Here’s the key information:

- Lian starts with **$100** in savings and adds **$40** per week.
- Nia starts with **$500** in savings and adds **$30** per week.
- The goal is to find when their savings will be equal.

The equation for Lian’s savings after $ w $ weeks is:
\[
100 + 40w
\]
The equation for Nia’s savings after $ w $ weeks is:
\[
500 + 30w
\]
We want to know when these two amounts will be equal, so we set the two equations equal to each other:
\[
100 + 40w = 500 + 30w
\]

### Solving for $ w $:
1. Subtract $ 30w $ from both sides:
   \[
   100 + 10w = 500
   \]
2. Subtract 100 from both sides:
   \[
   10w = 400
   \]
3. Divide by 10:
   \[
   w = 40
   \]

### Conclusion:
It will take **40 weeks** for Lian and Nia to have the same amount in savings.

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:
1. What if Lian added $50 per week instead of $40? How would this change the equation?
2. How much savings will both have after 40 weeks?
3. How many weeks would it take if Nia's initial savings were $600 instead of $500?
4. What would happen if Lian and Nia had different savings goals?
5. How can you modify the equation if both Lian and Nia decide to stop saving at different points?

**Tip:** When solving linear equations, always simplify both sides as much as possible before isolating the variable.

Lian has $100 in savings and adds $40 per week. Nia has $500 in savings and adds $30 per week. How many weeks until their savings are equal?

Learn how to solve a linear equation involving savings plans for Lian and Nia. Determine how many weeks it will take for their savings to be equal. This problem uses basic algebra and linear equations, suitable for students in Grades 9-10.

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