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Find all values of r such that \(\lfloor r \rfloor + r = 16.5\)

 Jun 20, 2020
 #1
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First, we note that r must be positive, since otherwise \(\lfloor r \rfloor + r\) is nonpositive. Next, because \(\lfloor r \rfloor + r\) is an integer and \( \lfloor r \rfloor + r=12.2\), the decimal part of r must be 0.5. Therefore, r=n+0.5 for some integer n, so that \(\lfloor r \rfloor + r\) and \(\lfloor r \rfloor + r = 2n+0.5 =16.5\). Therefore, n=8, and the only value of r that satisfies the equation is \(\boxed{r=8.5}\).

 Jun 20, 2020
 #2
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Thank you so much for helping with a lot of my problems!!!

AnimalMaster  Jun 20, 2020
 #3
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You're welcome.

gwenspooner85  Jun 20, 2020

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