https://file.aiquickdraw.com/mathbot/file/17293689768094can5jke.jpg

The problem in the image shows that James uses red tiles and black tiles to form square shapes. Here is a breakdown of the information provided:

1. A 3x3 shape contains:
   - 1 black tile
   - 8 red tiles (since 3x3 = 9 total tiles, and 9 - 1 = 8 red tiles)

2. A 4x4 shape contains:
   - 4 black tiles
   - 12 red tiles (since 4x4 = 16 total tiles, and 16 - 4 = 12 red tiles)

The question asks about a new shape that James made with a total of 64 tiles.

### Part a: What is the number of black tiles in this shape?
The shape has 64 total tiles. This is a perfect square, meaning it could be an 8x8 shape (since \(\sqrt{64} = 8\)).

From the given patterns:
- The 3x3 shape had 1 black tile.
- The 4x4 shape had 4 black tiles.

Noticing that the number of black tiles seems to increase in a quadratic manner (from \(1^2 = 1\) for the 3x3 shape to \(2^2 = 4\) for the 4x4 shape), we can deduce that for an 8x8 shape, the number of black tiles will be \(4^2 = 16\).

### Part b: What is the number of red tiles in this shape?
For an 8x8 grid:
- The total number of tiles is 64.
- The number of black tiles is 16 (as calculated).

Therefore, the number of red tiles will be:
\[
64 - 16 = 48 \text{ red tiles}.
\]

### Summary of Answers:
- a) Number of black tiles: 16
- b) Number of red tiles: 48

Would you like further details or clarifications? Here are five related questions:

1. What pattern do the black tiles follow in larger shapes?
2. How would the number of black and red tiles change in a 5x5 shape?
3. Can you identify the relation between the number of black tiles and the size of the shape?
4. What would the tile distribution look like for a 6x6 shape?
5. How do the numbers of black and red tiles scale as the shape size increases?

**Tip:** The number of black tiles in these square shapes follows a quadratic pattern, which can help predict the tile counts in larger shapes.

James made a shape with a total of 64 tiles. What is the number of black tiles and red tiles in the shape?

Learn how to find the number of black and red tiles in an 8x8 square with 64 tiles. Understand quadratic patterns in tile distribution, focusing on calculating tiles using side lengths and basic formulas. Suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation