The numbers were changed to protect the innocent.
I recently bought some books for my family on a holiday shopping trip. While standing in the checkout line, an overzealous gift wrapper covered my books in gold paper and ribbon before the cashier had rung up my purchase. Faced with the choice of undoing the gift wrapper's handiwork, the cashier and I decided instead to try to determine the prices of the books I wanted to purchase.
I had slipped my gift list (with the titles and authors) inside one of the books, so that information was unavailable. I did remember that the total cost of the books was $127. However, each one of the books I wanted to purchase was on sale, depending on its subject, and I had remembered the non-discounted total.
I had in my hands one of each of the following: cookbooks were 15% off, mysteries were 20% off, poetry was 25% off, biographies were 40% off, and architecture was 50% off. I also remembered that all of the prices were whole numbers, before and after their discounts had been applied.
With the following two clues, could the cashier and I determine how much the books would cost after the discounts had been applied?
- One book was $46 before its discount, another book was $20 before its discount.
- One book was $1 more than another book before the discounts were applied, but after the discounts, the books were the same price.