2019 Gauss 8 Problem 20

PQRS is a square with side length 60 and centre C. Point W lies on PS so that WS = 53. Point X lies on SR so that XR = 40. The midpoint of QR is Y. Point Z lies on PQ. What is the length of ZQ so that the total area of the shaded regions is equal to the total area of the non-shaded regions?

\textbf{(A)}\ 21\quad \textbf{(B)}\ 15\quad \textbf{(C)}\ 23\quad \textbf{(D)}\ 19\quad \textbf{(E)}\ 17

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Full credit to this problem is given to the CEMC, you may view all Gauss contests here.