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Wot n' Base Representation

Source: 2017 AIME I #5

March 8, 2017
2017 AIME I

Problem Statement

A rational number written in base eight is a‾b‾.c‾d‾\underline{a} \underline{b} . \underline{c} \underline{d}, where all digits are nonzero. The same number in base twelve is b‾b‾.b‾a‾\underline{b} \underline{b} . \underline{b} \underline{a}. Find the base-ten number a‾b‾c‾\underline{a} \underline{b} \underline{c}.
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