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As many brothers as sisters

algebrafamily-relationsclassic

A boy says: "I have as many brothers as sisters." His sister says: "I have twice as many brothers as sisters."

How many boys and how many girls are in the family? Set up the two statements carefully, remembering who is and is not counting themselves, and check your answer against both.

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When the boy counts his brothers, he does not count himself. When the sister counts her sisters, she does not count herself.

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The Substitution That Collapses the AlgebraFunctional EquationsNested Radicals and Infinite FractionsSolving Linear Recurrences With Characteristic RootsTelescoping Sums and Products

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