15. The sum of all zeros of the function $y=2(5-x) \sin \pi x-1(0 \leq x \leq 10)$ is equal to


Answer 60.
The zeros of the function $y=2(5-x) \sin \pi x-1(0 \leq x \leq 10)$ are the solutions to the equation $2(5-x) \sin \pi x-1=0$ in the interval $[0,10]$ $\Leftrightarrow$ the x-coordinates of the intersection points of the graph of the function $y=2 \sin \pi x$ and the graph of the function $y=\frac{1}{5-x}$ in the interval $[0,10]$.

Since the graph of the function $y=2 \sin \pi x$ and the graph of the function $y=\frac{1}{5-x}$ are both symmetric about the point $(5,0)$, and there are 12 intersection points (6 pairs of symmetric points) in the interval $[0,10]$, the sum of the coordinates of each pair of symmetric points is 10, i.e., the sum of the x-coordinates of these 12 points is 60, so the sum of all the zeros of the function $y=2(5-x) \sin \pi x-1(0 \leq x \leq 10)$ is 60.