Use the top-level ratio 9:4 to find how many paintings and sculptures there are, then break each group down using sub-ratios.
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• Top-level ratio 9:4 means 13 units in total.
• 52 ÷ 13 = 4 per unit.
• Paintings: 9 × 4 = 36
• Sculptures: 4 × 4 = 16
For the paintings (sub-ratio 2 + 1):
• 3 parts = 12 per part
• modern: 2 × 12 = 24
• classical: 1 × 12 = 12
For the sculptures (sub-ratio 1 + 3):
• 4 parts = 4 per part
• modern: 1 × 4 = 4
• classical: 3 × 4 = 12
Total modern: 24 + 4 = 28.
Check: 36 + 16 = 52 = total (52). ✓
Final Answer: 28