OK, so you have 40 boys and 30 girls. That’s easy enough to calculate because you’re given a part:whole ratio (boys to total students) and you already know the total number of students is 70.

Be careful about the second ratio, though, because it’s a part:part ratio! If the ratio of older to younger is 2:3, then the ratio of older to ALL STUDENTS is 2:5. (To figure this out, imagine that you only have 2 older kids and 3 younger kids). So you have 2/5*70 = 28 kids 10 or older, and 70 – 28 = 42 kids younger than 10.

To finally answer the question, we know 2/3 of the girls, or 20 girls, are less than 10. That means the other 42 – 20 = 22 kids younger than 10 must be boys.

If there are 40 boys, and 22 of them are younger than 10, then the other 18 must be 10 or older.

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