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Splitting 100 dollars between two siblings

Question

Jack and Jill share a $100 inheritance. If you subtract one-third of Jack's portion from one-quarter of Jill's portion, the result is $11. How much does Jack inherit?

Short answer

$24. With Jack's share nn, Jill gets 100−n100-n and 100−n4−n3=11\tfrac{100-n}{4}-\tfrac{n}{3}=11. Multiplying by 1212: 300−3n−4n=132300-3n-4n=132, so 7n=1687n=168 and n=24n=24.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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