$5\mathrm{.}3-15.$In considering medical insurance for a certain operation, let X equal the amount $($in dollars$)$ paid for the doctor and let Y equal the amount paid to the hospital. In the past, the variances have been Var$($X$)=8100,$ Var$($Y$)=10,000,$ and Var$($X$+$Y$)=20,000.$ Due to increased expenses, it was decided to increase the doctor's fee by $$500$ and increase the hospital charge Y by $8\%.$ Calculate the variance of X$+500+(1\mathrm{.}08)$Y$,$ the new total claim.