Non-uniform scaling

Question

I have 10 numbers $x_1, x_2, \dots, x_9, x_{10}$ which sum to a total of $1,000$.

I want to scale these numbers so the total is equal to $10,000$, however I don't want them to scale exactly.

I'm not sure exactly (will depend on the output) of the variance required in the scaling but I'm thinking somewhere $\approx10\%$.

Does this question make sense? Can anyone provide a solution on how to achieve this?

Thanks

Answer 1

1. Multiply each number by a randomly chosen real number between $9$ and $11$.
2. Scale the resulting numbers by the same factor to make their sum equal to $10000$.

If the result must be integer, add step (3) rounding and (4) adjusting some numbers by $\pm 1$ to bring the sum to $10000$ again, as necessary.