Use the top-level ratio 5:4 to find how many amateur and professional there are, then break each group down using sub-ratios.
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• Top-level ratio 5:4 means 9 units in total.
• 90 ÷ 9 = 10 per unit.
• Amateur: 5 × 10 = 50
• Professional: 4 × 10 = 40
For the amateur (sub-ratio 2 + 3):
• 5 parts = 10 per part
• win their first match: 2 × 10 = 20
• lose: 3 × 10 = 30
For the professional (sub-ratio 3 + 1):
• 4 parts = 10 per part
• win their first match: 3 × 10 = 30
• lose: 1 × 10 = 10
Total win their first match: 20 + 30 = 50.
Check: 50 + 40 = 90 = total (90). ✓
Final Answer: 50