美元美分混淆
Dollar Cent Confusion
题目详情
一名男子去银行兑现一张支票。柜员在给钱时不小心把“美元”当成“美分”，把“美分”当成“美元”给了他。他没有检查金额，直接回家，并花了 5 美分买糖。之后他发现自己剩下的钱正好是支票金额的两倍。去银行之前他身上一分钱都没有。问这张支票的金额是多少？
A man went to his local bank to cash a check. When giving his money to the cashier, by mistake, gave him dollars as cents and cents as dollars. He didn't examine the money and just walked home and spent a nickel on some candy. He then found that he possessed exactly twice as much money as the check was worth. He had no money in his pocket before going to the bank. How much was the check for?
解析
设支票面额为 美元，其中 是美元数， 是美分数。
他本应拿到 但柜员把美元和美分弄反了，所以他实际拿到的是
回家后他先花了 5 美分，因此剩下的钱为 根据题意，这正好是支票面额的两倍：
两边同乘 100 并整理，得到
再结合 ，可求得唯一整数解为
因此支票金额是 美元。
Original Explanation
He should have received Instead, dollars and cents were swapped, so he received
He spent 5 cents, so the amount left was
After spending the nickel, he had exactly twice the value of the check
Multiply both sides by 100 and rearrange:
Now look for integer solutions with
Trying values of , we find
Therefore the check was for dollars