Marina found a purse that regularly sells for $100 on the sale rack of her favourite store. The purse was marked down by 4096. A sign on the sale rack said "Take an additional 50% off sale prices today only." Marina is convinced that she will be saving $90 on this purchase.

a. How much will Marina actually pay for the purse?

b. If the retailer had really meant to sell the purse for $10, what discount rate would it have needed to advertise in the "today only" sale?