Question

约翰订购了 $4$ 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 $50\%$ 。原订单中黑袜双数与蓝袜双数之比为：

John ordered $4$ 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 $50\%.$ The ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order was:

$4:1$

$2:1$

$1:4$

$1:2$

$1:8$

答案：C

知识点：钱币比与比例一次方程

难度评级：1560

小提示：

设每双蓝袜价格为 $p$ ，原订单中蓝袜有 $n$ 双

Let a blue pair cost $p$ and let $n$ be the original number of blue pairs

大提示：

比较原账单 $(8+n)p$ 与调换数量后的账单 $(2n+4)p$

Compare the original bill $(8+n)p$ with the interchanged bill $(2n+4)p$

解答：

设每双蓝袜价格为 $p$ ，则每双黑袜价格为 $2p$ ；再设原订单中蓝袜有 $n$ 双。原账单为 $(8+n)p$ 。调换两种袜子的双数后，账单为 $(2n+4)p$ 。后者比前者多 $50\%$ ，所以 $2n+4=\frac32(n+8)\text{。}$ 因此 $n=16$ ，原订单中黑袜与蓝袜的双数之比为 $4:16=1:4$ 。

因此，正确答案是 C。

Let a blue pair cost $p,$ so a black pair costs $2p,$ and let $n$ be the original number of blue pairs. The original bill is $(8+n)p.$ After the quantities are interchanged, the bill is $(2n+4)p.$ The latter is $50\%$ greater, so $2n+4=\frac32(n+8).$ Thus $n=16,$ and the original black-to-blue ratio is $4:16=1:4.$

Thus, the correct answer is C.

1950 AMC 12 第 31 题

答案：C

难度评级：1560

小提示：

大提示：

解答：

其他年份的第 31 题