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The problem you posted asks:

**"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?"**

### Step-by-step Solution:

1. **Total Tiles**:
   Madeline has a total of:
   \[
   16 \text{ gray tiles} + 24 \text{ white tiles} = 40 \text{ tiles}.
   \]
   
2. **Arranging into Rows**:
   Since the tiles fit into a perfect rectangle, the number of rows must divide the total number of tiles evenly. To find the possible number of rows, we need to find the **common divisors** of 16 (gray tiles) and 24 (white tiles).

   The greatest common divisor (GCD) of 16 and 24 is **8**. Therefore, the number of rows should be **8** because this will allow an even distribution of gray and white tiles in each row.

3. **Tiles in Each Row**:
   If there are 8 rows, each row will have:
   \[
   \frac{16 \text{ gray tiles}}{8 \text{ rows}} = 2 \text{ gray tiles per row},
   \]
   and
   \[
   \frac{24 \text{ white tiles}}{8 \text{ rows}} = 3 \text{ white tiles per row}.
   \]

4. **Answer**:
   Madeline can arrange the tiles into **8 rows**, and each row will have **2 gray tiles and 3 white tiles**.

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Would you like further details or have any questions?

### Related Questions:
1. What is the importance of the greatest common divisor (GCD) in this problem?
2. How would the solution change if there were 18 gray tiles and 24 white tiles?
3. Can the tiles be arranged in fewer than 8 rows while still forming a perfect rectangle?
4. If Madeline wanted an equal number of gray and white tiles in each row, what would be the solution?
5. How can we generalize this approach for any number of gray and white tiles?

**Tip**: Always start by finding the GCD when distributing items into equal groups.

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?

Find out how to arrange 16 gray tiles and 24 white tiles into rows using the greatest common divisor (GCD) to form a perfect rectangle. This math problem is suitable for students in Grades 6-8 and covers divisibility and geometry concepts.

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