A shop owner raises the price of a $120 pair of shoes by 30%. After a few weeks, because of falling sales, the owner reduces the price of the shoes by 30%. A customer then says that the shoes are back at the original price.

a. What is the mistaken assumption here?

b. Why is that assumption incorrect?

c. What do the shoes actually cost now? Show calculation

d. By what percent should the shoes be decreased in order to have the price back at $120? Round to the nearest 10th percentage. (for example, if your decimal answer is .058267 your answer would be 5.8267% round to the nearest 10th percent answer is 5.8%) show calculation