Use the top-level ratio 5:2 to find how many adult and child there are, then break each group down using sub-ratios.

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• Top-level ratio 5:2 means 7 units in total.
• 70 ÷ 7 = 10 per unit.
• Adult: 5 × 10 = 50
• Child: 2 × 10 = 20

For the adult (sub-ratio 3 + 7):
• 10 parts = 5 per part
• with cavities: 3 × 5 = 15
• without: 7 × 5 = 35

For the child (sub-ratio 4 + 1):
• 5 parts = 4 per part
• with cavities: 4 × 4 = 16
• without: 1 × 4 = 4

Total with cavities: 15 + 16 = 31.

Check: 50 + 20 = 70 = total (70). ✓

Final Answer: 31