趣味的数学-64

某人收到一张支票，支票票面上写有一定数额的美元和美分。当他兑现支票时，银行出纳员把支票的美元和美分的数额弄颠倒了：美元的数额变为美分，美分的数额变为美元。此人花了$3.50后，意识到他所剩余的金额是原始支票金额的两倍。问原始支票的金额是多少？

【原文】

Somebody received a check, calling for a certain amount in dollars and cents. When he cashed the check, the teller made a mistake, paying him in dollars the amount written in cents, and vice-versa. Later after spending $3.50, he suddenly realized that he had twice the amount called for by the check. What was the amount on the check?

【引自 The American Mathematical Monthly [AMM]，1941，problem E430】