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Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

Given $a+2b+3c+4d+5e=k$ and $5a=4b=3c=2d=e$ , find the smallest positive integer value for $k$ so that $a$ , $b$ , $c$ , $d$ , and $e$ are all positive integers.

(A) $87$ (B) $522$ (C) $10$ (D) $120$ (E) $60$

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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.