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# If y + 2q = 15, q + 2p = 5 and p + 2y = 7, then ﬁnd the value of p + q + y.

$y+2q=15\\ y=15-2q\\\\ p+2y=7\\ p+2(15-2q)=7\\ p+30-4q=7\\ -3q+30=7\ \ \ |Subtract\ 30 \\ -3q=-23\ \ \ |Divide\ by\ -3\\ q=\frac{23}{3}\\\\ y=15-2q=15-2(\frac{23}{3})=15-\frac{29}{3}=15-7=8\\\\ p=7-2y\\ p=7-2*8\\ p=7-16=-9\\\\ \textbf{p+q+y=}-9+\frac{23}{3}+8=-1+7\frac{2}{3}=\boxed{6\frac{2}{3}}$