All five of your credit cards are stolen from your motel room while you are skiing. Fortunately you discover the loss within a few hours and immediately notify the credit card companies by telephone. On the following day, you also notify them by mail. However, later in the week, the thief uses your credit cards to charge $1,875 in purchases. Eventually, each credit card company bills you for $50 of the purchases made with its card. By what authority did they do this? Must you pay these bills?