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Let's solve the given problem step by step.

### Problem:
We are given:
1. \( m, n, p \) are integers.
2. \( p + 3m = n \).
3. We need to determine the value of \( m + n - p \).

### Step-by-step solution:

1. From the equation \( p + 3m = n \), we can solve for \( n \):
   \[
   n = p + 3m
   \]

2. We are asked to find the value of \( m + n - p \). Substituting \( n = p + 3m \) into this expression:
   \[
   m + n - p = m + (p + 3m) - p
   \]
   Simplifying the expression:
   \[
   m + n - p = m + p + 3m - p = 4m
   \]

3. Therefore, the expression \( m + n - p \) simplifies to \( 4m \).

4. Now, the problem asks which value \( 4m \) could take from the given options: 10, 18, 24, 34, 42.

   Since \( m \) is an integer, we solve for \( m \) by dividing each option by 4:
   - \( 10 \div 4 = 2.5 \) (Not an integer)
   - \( 18 \div 4 = 4.5 \) (Not an integer)
   - \( 24 \div 4 = 6 \) (This is an integer)
   - \( 34 \div 4 = 8.5 \) (Not an integer)
   - \( 42 \div 4 = 10.5 \) (Not an integer)

### Conclusion:
The only possible value for \( m + n - p = 4m \) that satisfies the condition of \( m \) being an integer is when \( 4m = 24 \), which gives \( m = 6 \).

Thus, the correct answer is **C) 24**.

Would you like any more details, or do you have further questions? Here are five related questions to expand on this concept:

1. What happens if we have different coefficients instead of \( 3m \) in the equation \( p + 3m = n \)?
2. How can this method be extended to solve other linear equations involving three variables?
3. What if \( m, n, p \) were required to be non-integers? How would the solution change?
4. How would you solve if \( m + n - p \) was instead \( m + n + p \)?
5. Can you provide a real-life scenario where such linear equations could be applied?

**Tip**: When solving equations, always simplify expressions step by step to avoid errors and achieve clarity.

m, n, p birer tam sayıdır. p + 3m = n olduğuna göre, m + n - p değeri hangisi olabilir?

Learn how to solve for m + n - p given that p + 3m = n, where m, n, and p are integers. This step-by-step solution simplifies the equation and evaluates the possible integer results, making it suitable for students in Grades 8-10.

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