Pat went into a bank to cash a check that was for less than $100. The clerk gave Pat bills and coins. Counting the handout, Pat noticed that the clerk had made a mistake, exchanging the number of dollars for the number of cents, and vice versa. Then Pat dropped a nickel (5 cents) on the floor. Surprisingly, the remaining amount (that is, without the nickel) was exactly twice the correct value of the check. How much was the check for? Hint: compute the value of the check as 100x+y, where x is the dollar amount and y is the penny amount, both integers.