To solve this problem, let’s carefully analyze the information provided.

1. Initial Ratio of Marbles:

   • The initial ratio of the number of marbles Farhan had to the number of marbles Junhao had is $3 : 4$.

2. Change in Marbles:

   • After Farhan bought 15 more marbles, the ratio of Farhan's marbles to Junhao's marbles became $3 : 2$.
   • It's important to note that only Farhan’s number of marbles changed; Junhao's marbles remained the same throughout the process.

3. Setting Up the Equations:

   • Let $3x$ represent the initial number of marbles Farhan had, and $4x$ represent the initial number of marbles Junhao had.
   • After Farhan buys 15 more marbles, his number of marbles becomes $3x + 15$.
   • According to the new ratio $3 : 2$, we can write the equation: $\frac{3x + 15}{4x} = \frac{3}{2}$

4. Solving the Equation:

   • Cross-multiplying gives: $2(3x + 15) = 3(4x)$
   • Expanding both sides: $6x + 30 = 12x$
   • Rearranging terms: $30 = 6x$
   • Solving for $x$: $x = 5$

5. Calculating the Initial Number of Marbles:

   • Substituting $x = 5$ back into the expressions for Farhan’s and Junhao’s marbles:
     • Farhan’s initial marbles = $3x = 3 \times 5 = 15$
     • Junhao’s initial marbles = $4x = 4 \times 5 = 20$

6. Total Number of Marbles Initially:

   • The total number of marbles Farhan and Junhao had together initially is: $15 + 20 = 35$

Answer: Farhan and Junhao had a total of 35 marbles initially.

Would you like a deeper explanation on any of these steps?

Here are five follow-up questions that build on this topic:

1. If Farhan had bought 10 more marbles instead of 15, would the ratio change?
2. How would the solution differ if the initial ratio was given as $4 : 5$?
3. What if both Farhan and Junhao increased their marbles by the same amount? How would the final ratio change?
4. Can you generalize a formula for situations where two quantities are in a ratio and one quantity changes?
5. What is the impact of proportional changes on the ratios in a different context, such as distance or speed?

Tip: Ratios can be scaled up or down by a common factor, but solving for unknowns often requires setting up equations based on the conditions given.