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Solve floor(r) + r = 12.2 - r.

 May 2, 2022
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We have \(\lfloor r \rfloor = 12.2 - 2r\). Then 12.2 - 2r must be an integer. Then \(r = k + 0.1\text{ or }r = k + 0.6\) for some integer k. Now you can substitute that and try to solve it like a linear equation.

 May 2, 2022

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