https://file.aiquickdraw.com/mathbot/file/1726707774505wjzz2euv.jpg

To solve the problem, let's break it down step by step:

### Problem Statement:
Liam and Mia are competing to see who can read more books. 
- Liam has already read **5 books** and plans to read **2 more books each week**.
- Mia has already read **3 books** and plans to read **3 more books each week**.

We need to find out how many weeks (**x**) it will take for Liam and Mia to have read the **same number of books**.

### Equation Setup:
Let **x** represent the number of weeks they read.

- For Liam: After **x** weeks, he will have read:
  \[
  5 + 2x
  \]
  (5 books initially + 2 books per week).

- For Mia: After **x** weeks, she will have read:
  \[
  3 + 3x
  \]
  (3 books initially + 3 books per week).

### Setting up the equation:
To find when they have read the same number of books, we need to set their total books equal to each other:
\[
5 + 2x = 3 + 3x
\]

### Solving the equation:
Let's solve for **x**.

\[
5 + 2x = 3 + 3x
\]
Subtract **2x** from both sides:
\[
5 = 3 + x
\]
Subtract **3** from both sides:
\[
2 = x
\]

### Solution:
So, Liam and Mia will have read the same number of books after **2 weeks**.

### Final Answer:
- The equation that represents the situation is:
  \[
  5 + 2x = 3 + 3x
  \]
- Liam and Mia will have read the same number of books after **2 weeks**.

---

Do you have any questions or would you like further details on any step? Here are 5 related questions you might explore:

1. How many total books will Liam and Mia each have read after 2 weeks?
2. If Mia started reading 1 book more per week than Liam, how would the equation change?
3. What would happen if Liam read 1 more book initially?
4. How can this problem be modeled graphically, and what does the intersection represent?
5. How would the solution change if Liam read at a faster pace (e.g., 4 books per week)?

**Tip:** Always isolate the variable by performing the same operation on both sides of the equation!

Liam and Mia are competing to see who can read more books over the summer. Liam has already read 5 books and plans to read 2 more each week. Mia has read 3 books but plans to read 3 more each week. After how many weeks will they have read the same number of books?

Learn how to solve a linear equation problem where Liam and Mia compete to read books over the summer. Liam reads 5 books and adds 2 books each week, while Mia starts with 3 books and reads 3 more per week. After 2 weeks, they will have read the same number of books.

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