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Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

Three different numbers are chosen such that when each of the numbers is added to the average of the remaining two, the numbers 65, 69 and 76 result. The average of the three original numbers is

(A) $34$ (B) $35$ (C) $36$ (D) $37$ (E) $38$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.