### Instruction: The average of the numbers $1, 2, 3,\dots, 98, 99,$ and $x$ is $100x$. What is $x$?### Response: So we want to find the average of the numbers $1$ to $99$ and $x$.
That means we want to find $\frac{1+2+\dots+98+99+x}{100}$.
The numbers $1$ to $99$ add up to $\frac{99\cdot100}{2}=4950$.
So we have $\frac{4950+x}{100}=100x$.
Multiplying both sides of the equation by $100$ we get $4950+x=10000x$.
Subtracting $x$ from both sides we get $4950=9999x$.
Finally dividing by $9999$ we get $x=\frac{4950}{9999}$.
That's a weird number.