7. When the point $(x, y)$ moves on the curve $\frac{(x-5)^{2}}{16}+\frac{y^{2}}{9}=1$, the sum of the maximum and minimum values that the algebraic expression $\frac{x^{2}}{16}+\frac{y^{2}}{9}$ can take is


7. $\frac{41}{8}$.