Say a sandwich is made of one slice of cheese, three slices of ham, and two slices of bread, and that cheese is X% off, ham is Y% off,and bread is Z% off. I don't know what the actual price of anything is; just the percent discounts. What percent discount am I getting on my entire sandwich? Is this even solvable?
Intuitively I thought the discount of the total was the mean of the discounts of the components times what fraction the discounted part is of the whole ($discount = (1X + 3Y + 2Z)/3$), but it looks like that's only true if the price of the components are all equal, or the discounts are all equal, and neither of those things are true of the real problem I'm trying to solve.
If you want a plain number then you need the prices. Otherwise you can still express the total discount via a formula and plug in the prices once you have those. The formula is $$1-\frac{(1-d_c)c+(1-d_h)h+(1-d_b)b}{c+h+b}$$ where for example $h$ stands for ham and $d_h$ is the discount on ham.
Note that this is nothing but a weighted average.