The sum of the discount is the discount of the sum Suppose I have a till. I have a special that I give a 10 percent discount on all dinner meals. I want to know that if I calculate the discount on each dinner item and round up the discount and apply it to each meal, I will not lose money than if I first added up the dinner items and then applied the 10 percent discount and then rounded up the answer.

The consumer benefits from roundup of individual meals because $$\lceil .1(x_1+x_2+\cdots +x_n)\rceil \le \lceil .1 x_1\rceil + \lceil .1 x_2\rceil + \cdots + \lceil .1 x_n\rceil$$ where $\lceil\quad\rceil $ is the ceiling function. So if you're the restauranteur you'd prefer to round up after totaling the meals.