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The problem reads:

**"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?"**

### Solution:

We need to figure out how Madeline can arrange the tiles into rows so that:
1. **Each row has the same number of tiles.**
2. **All tiles fit into the rectangle perfectly (without remainder).**
3. **Each row has a consistent pattern (equal number of gray and white tiles distributed evenly).**

#### Step 1: Total number of tiles
Madeline has:
- 16 gray tiles
- 24 white tiles

The total number of tiles = \( 16 + 24 = 40 \) tiles.

#### Step 2: Finding the number of rows (divisors of 40)
We need to divide the total 40 tiles into equal rows. The number of **rows** must be a divisor of 40, since the tiles fit exactly into a rectangle. The divisors of 40 are:

\[
1, 2, 4, 5, 8, 10, 20, 40
\]

So, possible options for the number of rows are: 1, 2, 4, 5, 8, 10, 20, or 40.

#### Step 3: Check each divisor for feasible arrangements of gray and white tiles
We must ensure that both the 16 gray tiles and 24 white tiles are evenly distributed among the rows. This means that the number of **gray tiles per row** and **white tiles per row** must be integers.

Now, we try a few cases:

- **Case: 4 rows**
  - Gray tiles per row: \( 16 \div 4 = 4 \)
  - White tiles per row: \( 24 \div 4 = 6 \)
  
  This is a valid arrangement! Each row will have **4 gray tiles** and **6 white tiles**, making 10 tiles per row.

#### Step 4: Final Arrangement
With **4 rows**, each row will contain:
- 4 gray tiles
- 6 white tiles

Each row will therefore contain a total of \( 4 + 6 = 10 \) tiles.

### Answer:
Madeline can arrange the tiles into **4 rows**.  
Each row will have **4 gray tiles and 6 white tiles**.

---

Do you want a deeper breakdown or other divisor cases explored?  
Here are 5 related questions to explore:

1. What if Madeline wanted the number of gray and white tiles per row to be equal?
2. Can the tiles be arranged into 5 rows? What would that look like?
3. How many total unique rectangular arrangements are possible?
4. What is the area of the rectangle if each tile is 1 unit by 1 unit?
5. How can the tiles be rearranged to form a square grid?

**Tip:** Always start by breaking problems with "rectangular arrangements" by finding common divisors!

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 rectangular shape. This problem explores finding divisors and creating a balanced arrangement. Suitable for students in Grades 5-7.

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