Question 1194368
Certainly, let's break down the problem and find the sum of all possible values of 'm'.

**1. Define Variables:**

* Let 'x' be the number of samples containing blueberries.
* Let 'y' be the number of samples not containing blueberries. 

**2. Set up Equations**

* **Total Samples:** x + y = 4200 
* **Student B Reports More Blueberries:** 
    * 0.98x - 0.90x = 315 
    * 0.08x = 315
    * x = 3937.5

* **Since the number of samples must be whole numbers:**
    * x = 3938 
    * y = 4200 - 3938 = 262

**3. Determine the Number of Samples Reported as Containing Blueberries by Each Student:**

* **Student A:** 0.90x = 0.90 * 3938 = 3544.2 ≈ 3544 
* **Student B:** 0.98x = 0.98 * 3938 = 3861.24 ≈ 3861
* **Student C:** (2m/100) * x = (2m/100) * 3938 = 78.76m ≈ 78.76m

**4. Find the Total Number of Samples Reported as Containing Blueberries by All Students:**

* Total = Student A + Student B + Student C
* Total = 3544 + 3861 + 78.76m 
* Total = 7405 + 78.76m

**5. Determine the Range for Total Samples Containing Blueberries**

* The total number of samples reported as containing blueberries is a multiple of 5 between 8000 and 9000.
* Therefore: 
    * 8000 ≤ 7405 + 78.76m ≤ 9000
    * 595 ≤ 78.76m ≤ 1595

**6. Find Possible Values of 'm'**

* 595 / 78.76 ≤ m ≤ 1595 / 78.76
* 7.55 ≤ m ≤ 20.23

* Since 'm' is a positive integer:
    * Possible values of 'm': 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

**7. Calculate the Sum of All Possible Values of 'm'**

* Sum = 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 
* Sum = 153

**Therefore, the sum of all possible values of 'm' is 153.**