Question 21
Given the equation
$$\left\lceil\frac{x}{2}\right\rceil+\left\lceil\frac{x}{5}\right\rceil+\left\lceil\frac{x}{10}\right\rceil=x,$$
where $\lceil t\rceil$ denotes the least integer greater than or equal to $t$, find the number of positive integers $x\lt10500$ satisfying the equation.
For example, $\lceil2.7\rceil=3$ and $\lceil-3.2\rceil=-3$.
$$\left\lceil\frac{x}{2}\right\rceil+\left\lceil\frac{x}{5}\right\rceil+\left\lceil\frac{x}{10}\right\rceil=x,$$
where $\lceil t\rceil$ denotes the least integer greater than or equal to $t$, find the number of positive integers $x\lt10500$ satisfying the equation.
For example, $\lceil2.7\rceil=3$ and $\lceil-3.2\rceil=-3$.