We use your analysis. We paid an extra $90$ cents. For that, we could ship a package that weighs $250+ \frac{90}{10}(100)$ grams, that is, $1150$ grams.
But note that the fine print says that we pay $10$ cents for every $100$ grams or part thereof. So if we are "over" the basic $250$ grams, say by $802$ grams, we pay $80$ cents for the $800$ grams, and an extra $10$ cents for the measly $2$ extra grams over $800$. In effect, we are paying as if our package weighed $250+900$. (So we might as well open the package and put a couple of cookies in. The shipping cost won't change.)
Mathematically, all one can say is that if we paid $\$1.55$ to ship the package, then the weight $w$ of the package satisifes the inequality $250+800 \lt w \le 250+900$, that is, $1050 \lt w \le 1150.$ If the question was a multiple choice question, and $1145$ was the only "answer" supplied that is in the above interval, then $1145$ is the right answer.