https://file.aiquickdraw.com/mathbot/file/1726552433572miqhzabj.jpg

The problem states:

- Madeline has 16 gray tiles and 24 white tiles. 
- She fits them into a rectangle exactly. 
- The questions are: 
  - How many rows of tiles can she arrange? 
  - What are the colors on each row?

### Step-by-Step Solution:

1. **Total Tiles**:  
   Madeline has \( 16 \) gray tiles and \( 24 \) white tiles. The total number of tiles is:
   \[
   16 + 24 = 40 \text{ tiles}.
   \]

2. **Rectangle Configuration**:  
   To fit these 40 tiles into a rectangle exactly, the number of tiles in each row must divide 40 evenly.

   First, find the factors of 40:  
   \( 40 = 1 \times 40 \), \( 2 \times 20 \), \( 4 \times 10 \), and \( 5 \times 8 \).

   These factor pairs correspond to possible row-column arrangements:  
   - 1 row of 40 tiles  
   - 2 rows of 20 tiles  
   - 4 rows of 10 tiles  
   - 5 rows of 8 tiles  
   - 8 rows of 5 tiles  
   - 10 rows of 4 tiles  
   - 20 rows of 2 tiles  
   - 40 rows of 1 tile  

3. **Distributing Colors**:  
   Now, we need to ensure that both the gray and white tiles are distributed evenly across rows. Let's analyze a few possibilities:

   - **4 rows of 10 tiles**:  
     If we have 4 rows, each with 10 tiles:
     - Total gray tiles = 16 tiles. Dividing these evenly into 4 rows gives \( 16 \div 4 = 4 \) gray tiles per row.
     - Total white tiles = 24 tiles. Dividing these evenly into 4 rows gives \( 24 \div 4 = 6 \) white tiles per row.
     
     Therefore, in this case, there are **4 rows**, each containing **4 gray tiles** and **6 white tiles**.

### Final Answer:
- **Number of rows**: 4 rows.
- **Tiles in each row**: Each row will have 4 gray tiles and 6 white tiles.

Would you like more details or have any questions about this problem?

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Here are 5 related questions you might find useful:
1. What is the greatest common divisor (GCD) of 16 and 24?
2. How do you determine the total number of tiles from multiple types?
3. What other rectangle configurations could work with 16 gray and 24 white tiles?
4. How does the ratio of gray to white tiles change if you increase the number of rows?
5. Can you use these tile arrangements to form different geometric shapes?

**Tip**: When working with problems involving tiling or arranging items into rows, always check if the total number of items is divisible by possible row numbers to ensure the arrangement fits perfectly!

Madeline has 16 gray tiles and 24 white tiles. She fits them into a rectangle exactly. How many rows of tiles can she arrange and what are the colors on each row?

Learn how to arrange 16 gray tiles and 24 white tiles into a rectangle with rows and evenly distributed colors. This problem involves basic factorization and tile arrangement. Suitable for Grades 5-7.

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