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Let's analyze and solve this problem step-by-step.

### Problem Breakdown
Rudi starts with **120 marbles** and distributes them as follows:
1. To **Bima**: a certain unspecified amount.
2. To **Sultan**: **30%** of his marbles.
3. To **Jaka**: **0.15** of his marbles.
4. The remainder is split equally between **Rudi himself** and **Satriya**.

Finally, **10 marbles from Satriya** are returned to Rudi. We are asked to find the largest difference between the number of marbles Rudi has after the transaction and the number held by any of his friends.

### Solution Steps

1. **Calculate marbles given to Bima, Sultan, and Jaka**:
   - Let \( x \) be the number of marbles given to Bima.
   - Marbles given to **Sultan** = \( 0.3 \times 120 = 36 \) marbles.
   - Marbles given to **Jaka** = \( 0.15 \times 120 = 18 \) marbles.

2. **Determine Remaining Marbles after Distribution**:
   - After giving marbles to Bima, Sultan, and Jaka, the remaining marbles are:
     \[
     120 - (x + 36 + 18) = 66 - x
     \]

3. **Distribute Remaining Marbles Between Rudi and Satriya**:
   - The remaining marbles \( (66 - x) \) are split equally between Rudi and Satriya. Therefore:
     \[
     \text{Marbles each for Rudi and Satriya} = \frac{66 - x}{2}
     \]

4. **Adjust Rudi's Marbles after Receiving 10 Marbles from Satriya**:
   - Satriya gives **10 marbles** back to Rudi, so Rudi's final count becomes:
     \[
     \text{Rudi's final marbles} = \frac{66 - x}{2} + 10
     \]

5. **Determine the Maximum Difference**:
   - We need to find the difference between Rudi’s final marble count and each friend's count, then identify the maximum difference.
   
Would you like me to calculate each friend's count explicitly and find this maximum difference? 

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### Questions for Deeper Understanding:
1. How is percentage calculation relevant in determining shares in practical situations?
2. What are possible reasons for splitting items equally after giving away portions?
3. Why is it important to calculate remaining amounts after initial distributions in such problems?
4. How does adding back some items to one person affect final distributions?
5. In what real-life situations can such distribution calculations be applied?

### Tip:
When dealing with percentages and fractions in word problems, translate them immediately into their decimal or fractional form for clearer calculations.

Rudi akan bermain kelereng bersama Bima, Sultan, Jaka dan Satriya. Rudi memiliki 120 kelereng. Rudi akan membagikan kelerengnya kepada Bima; 30% kelereng kepada Sultan dan 0,15 bagian kepada Jaka. Sisa kelereng Rudi akan dibagi sama banyak untuk dirinya sendiri dan Satriya. Jika 10 kelereng Satriya diberikan kembali kepada Rudi, berapakah selisih paling banyak antara kelereng yang dimiliki Rudi dengan kelereng milik masing-masing temannya?

Pelajari cara menentukan selisih paling banyak antara jumlah kelereng yang dimiliki Rudi dengan masing-masing temannya dalam soal pembagian kelereng. Soal ini mencakup konsep persentase, pecahan, dan distribusi sisa yang cocok untuk siswa kelas 6-8.

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