Square $PQRS$ lies in the first quadrant. Points $(3,0)$, $(5,0)$, $(7,0)$, and $(13,0)$ lie on lines $SP$, $RQ$, $PQ$, and $SR$, respectively. If the sum of the coordinates of the center of the square $PQRS$ is $x$, what is the value of $10x$?

Let's think step by step and output the final answer within \boxed{}.
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