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Problem 375

Algebra Difficulty 2.0 Prove it UKMT Junior Mathematical Olympiad · United Kingdom · 2018

Polly Garter had her first child on her 20th birthday, her second child exactly two years later, and her third child exactly two years after that. How old was Polly when her age was equal to the sum of her three children's ages?

This one wants a proof. Work it on paper, then check yourself against the publisher's own solution, linked below. Be honest about it: the record is only any use to you if it is.

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.