1950 AMC 12 第 31 题
先试着解答 1950 AMC 12 第 31 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1950 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
31.
约翰订购了 双黑袜和若干双蓝袜。每双黑袜的价格是蓝袜的两倍。配货时，两种颜色袜子的双数被调换了，导致账单金额增加 。原订单中黑袜双数与蓝袜双数之比为：
John ordered pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of the two colors had been interchanged. This increased the bill by The ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order was:
小提示：
设每双蓝袜价格为 ，原订单中蓝袜有 双
Let a blue pair cost and let be the original number of blue pairs
大提示：
比较原账单 与调换数量后的账单
Compare the original bill with the interchanged bill
解答：
设每双蓝袜价格为 ，则每双黑袜价格为 ；再设原订单中蓝袜有 双。原账单为 。调换两种袜子的双数后，账单为 。后者比前者多 ，所以 因此 ，原订单中黑袜与蓝袜的双数之比为 。
因此，正确答案是 C。
Let a blue pair cost so a black pair costs and let be the original number of blue pairs. The original bill is After the quantities are interchanged, the bill is The latter is greater, so Thus and the original black-to-blue ratio is
Thus, the correct answer is C.