A torque balance that is $10\mathrm{.}0$ m long and has a mass of $10\mathrm{.}0$ kg is used to compare the weight of a $52\mathrm{.}1$ kg witch to that of a $1\mathrm{.}69$ kg duck. The witch and duck are placed at opposite ends of the balance, at distances $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ from the pivot point P$.($See the sketch below.$)$ Determine the distance $\backslash ($ y $\backslash )$ such that the system is balanced.

a$)10\mathrm{.}6$ m

b$)9\mathrm{.}53$ m

c$)8\mathrm{.}76$ m

d$)5\mathrm{.}00$ m

e$)7\mathrm{.}38$