# Numbers and Reciprocals

Algebra Level 4

Three positive real numbers $$p,q,r$$ satisfy

$\begin{eqnarray} \frac { 1 }{ p } +q &=& 2\\ \frac { 1 }{ q } +r &=& 3\\ \frac { 1 }{ r } +p &=& 5\\ \end{eqnarray}$

Find the sum of all possible values of $$p$$.

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