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The average of three positive integers is $28$. When two additional integers, $s$ and $t$, are included, the average of all five integers is $34$. What is the average of $s$ and $t$?

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