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Weighing a fish from its head, body and tail

Question

A fish is cut into three parts. Its tail weighs 99 ounces. Its head weighs as much as the tail plus half of the body. Its body weighs as much as the head and tail combined. What does the whole fish weigh, in ounces?

Short answer

7272 ounces. With h=9+b2h=9+\tfrac b2 and b=h+9b=h+9, substitution gives b=18+b2b=18+\tfrac b2, so b=36b=36, h=27h=27, and 9+27+36=729+27+36=72.

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

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