A store had a sale on eggs, selling 13 eggs for the usual price of a dozen eggs. As a result, the price of the eggs was reduced by 4 cents a dozen. What is the original price for a dozen eggs?

The key here is to think of the problem in a slightly different way. Suppose that, rather than giving you a bonus egg, the store owner reduced the price of the eggs so that you can now buy 13 eggs for what it formerly cost for 12 eggs. If you buy a dozen eggs at the new price then this is 4 cents less than a dozen eggs at the old price. But money for a dozen at the old price will buy you 13 eggs at the new price. Thus the 4 cents buys one more egg at the new price. Hence, at the new price, you can buy 13 eggs for 13x4 = 52 cents. But this is what it costs for a dozen eggs at the old price.