https://file.aiquickdraw.com/mathbot/file/1727380633853fxefolyg.jpg

Let's break down the exercises in the image and go through them one by one:

### Exercise 1:
- You're given three numbers: \( X \), \( Y \), and \( Z \).
- The task is to substitute the numbers given in the grid into the equation \( X + Y + Z \).

#### Grid:
| X | Y | Z |
|---|---|---|
| 6 | 5 | 4 |
| 7 | 9 | 2 |

For each row, the equation \( X + Y + Z \) should be calculated:
1. First row: \( 6 + 5 + 4 = 15 \)
2. Second row: \( 7 + 9 + 2 = 18 \)

In the example solved in the worksheet, the equation \( X + Y + Z = 109 \) seems incorrect. However, let’s focus on the calculations as intended based on the numbers provided.

### Exercise 2:
- There are two numbers (presumably X and Y) with the same difference between them and the number 207.

- The subtraction for the second row gives \( 207 - X = Y \). Using the provided operations, we calculate how this pattern works.

### Exercise 3:
- This section asks for finding the rule and filling in the missing values. The following operations are shown:
   1. \( (8 - 9) : 2 = 36 \)
   2. \( (99 - 27) : 2 = 36 \)

The rule is \( c = 6 \), derived from the consistent results of 36.

Another part of this exercise involves a more complex equation:
- \( (56 + 34) : x = 75 \)

It seems we're solving for the unknown \( x \), but I’d need more details on the precise setup.

Would you like me to work through a specific part of the image or verify my interpretation of the task?

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Here are five related questions to help you understand this better:

1. What pattern can you identify in the second exercise between the given numbers?
2. How could you generalize the rule used in Exercise 3 for other problems?
3. Can you verify if all calculations for Exercise 1 are correct?
4. How would you approach the last equation in Exercise 3? 
5. What other arithmetic patterns might apply to the missing numbers in the puzzles?

**Tip:** Always check if there is a consistent mathematical relationship between numbers when solving puzzles like these.

The user submitted a math worksheet containing three exercises, focusing on algebraic operations, arithmetic rules, and pattern identification.

This worksheet covers basic algebraic and arithmetic problems, including sum calculations, pattern recognition, and simple division. Ideal for students in grades 5-7 to practice mathematical concepts.

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