At a school event, adults are seated in groups of exactly 2 and children are seated in groups of exactly 12. If there are the same number of adults as children, what is the minimum number of adults attending?
Question
At a school event, adults are seated in groups of exactly 2 and children are seated in groups of exactly 12. If there are the same number of adults as children, what is the minimum number of adults attending?
Solution
The minimum number of adults attending would be 24. Here's why:
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Since adults are seated in groups of 2, the minimum number of adults would be 2 (one group).
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However, the problem states that there are the same number of adults as children.
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Children are seated in groups of 12, so the minimum number of children would be 12 (one group).
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But since the number of adults and children must be the same, and the minimum number of children is 12, the minimum number of adults must also be 12.
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However, adults are seated in groups of 2, so the number of adults must be a multiple of 2.
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The smallest multiple of 2 that is equal to or greater than 12 is 24.
So, the minimum number of adults attending is 24.
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