https://file.aiquickdraw.com/mathbot/file/17280055411791gzubo80.jpg

We need to set up an equation to solve this problem. Here's how we approach it:

- Megan starts with $50 and saves $5.50 per week.
- Connor starts with $18.50 and saves $7.75 per week.

We need to find out after how many weeks, $ x $, they will have saved the same amount.

Let’s define the total amount each will have after $ x $ weeks:

- Megan’s savings after $ x $ weeks: $ 50 + 5.50x $
- Connor’s savings after $ x $ weeks: $ 18.50 + 7.75x $

To find when they will have saved the same amount, we set these two expressions equal to each other:

\[
50 + 5.50x = 18.50 + 7.75x
\]

### Solving the equation:
1. Subtract $ 5.50x $ from both sides:
\[
50 = 18.50 + 2.25x
\]
2. Subtract 18.50 from both sides:
\[
31.50 = 2.25x
\]
3. Divide both sides by 2.25:
\[
x = \frac{31.50}{2.25} = 14
\]

So, it will take 14 weeks for Megan and Connor to have saved the same amount of money.

Would you like a deeper explanation or have any further questions?

Here are five related questions for practice:
1. How much will Megan and Connor have saved after 14 weeks?
2. What if Megan saved $6 per week instead of $5.50? How would that change the number of weeks?
3. How much more will Connor have saved than Megan after 10 weeks?
4. If Megan starts saving 2 weeks earlier, how long will it take for them to save the same amount?
5. How much will Connor have saved after 20 weeks?

**Tip:** In word problems involving savings or growth over time, setting up equations with variables is a great way to solve for unknowns efficiently.

Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will Megan and Connor have saved the same amount?

Solve a linear equation problem where Megan saves $5.50 each week starting from $50 and Connor saves $7.75 each week starting from $18.50. Find out how many weeks it will take for them to save the same amount.

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