Two different types of cake are on sale at prices of $0.30 and $0.40 each. The cakes that are being sold for $0.30 cost $0.20 to make and the ones for sale at $0.40 cost $0.25 to make. No cakes can be kept to be sold the next day, so all of the cakes are reduced to half price 2 hours before the sales finish. All of the $0.30 cakes sold out before any of the prices were reduced, and all of the $0.40 were eventually sold, even though only half had been sold when the price was reduced. The overall profit at the end of the day was $30.00, but it could have been $40.00 if all of the cakes had sold before the prices were reduced. How many of each type of cake were there in the sale?
