We can solve this problem by using the concept of weighted averages.

Let:

• $x$ = the number of students who passed the examination.
• $y = 120 - x$ = the number of students who failed the examination.

Step 1: Formulate the total marks of passed and failed students.

We know that the total marks for all students is the sum of the marks of the passed and failed students.

Given:

• The average marks of passed students = 39
• The average marks of failed students = 15
• The total number of students = 120
• The overall average = 35

Thus, the total marks obtained by the passed students is: $\text{Total marks of passed students} = 39 \times x$ And the total marks obtained by the failed students is: $\text{Total marks of failed students} = 15 \times (120 - x)$

Step 2: Set up the equation for total marks.

Since the overall average is 35, the total marks obtained by all 120 students is: $\text{Total marks of all students} = 35 \times 120 = 4200$

We also know that the total marks is the sum of the marks of passed and failed students, so: $39x + 15(120 - x) = 4200$

Step 3: Solve for $x$.

Simplifying the equation: $39x + 1800 - 15x = 4200$ $24x + 1800 = 4200$ $24x = 4200 - 1800$ $24x = 2400$ $x = \frac{2400}{24} = 100$

Thus, the number of students who passed the examination is $\boxed{100}$.

Would you like further details or have any questions?

Here are some related questions:

1. What if the average of failed students was higher, say 20?
2. How would the result change if the total number of students was different?
3. Can you calculate the passing rate as a percentage?
4. What if we don't know the overall average but have the total marks?
5. How does the problem change if there were 5 more failed students?

Tip: In weighted average problems, the total value is distributed according to the proportion of groups.