Will you get the same discount either way? Is there a property of arithmetic related to this? Explain!

Question

Your factor store is having a 10%-off sale, meaning that the store will take 10% off the price of each item you buy. When the clerk rings your purchases, she takes 10% off the total (before tax) rather than 10% off each item. Will you get the same discount either way? Is there a property of arithmetic related to this? Explain

Answer 1

Yes, it is called the Distributive Property of Multiplication over Addition.

0.10x + 0.10y + 0.10z = 0.10(x + y + z)