Solution:

Take one coin from the first bag, 2 from the second, 3 from the third, ..., 10 from the 10th and place them on the scale. The total mass shown by the scale should be $$(1+2+\cdots+10) \cdot 10 - x$$ grams, where $x$ is the number of fake coins (each coin weighs 10 grams, except for the fake ones that are one gram lighter). Since the scale will show $550 - x$ grams, we can see how many coins are fake and that is enough to deduce from which bag those coins were taken.