Question

一名商人按每 $3$ 个 $10$ ¢ 的价格买入一些橙子，又按每 $5$ 个 $20$ ¢ 的价格买入同样多的橙子。为了“收支相抵”，他必须把所有橙子按下列哪个价格卖出？

A merchant buys a number of oranges at $3$ for $10$ ¢ and an equal number at $5$ for $20$ ¢. To “break even” he must sell all at:

每 $8$ 个 $30$ ¢

$8$ for $30$ ¢

每 $3$ 个 $11$ ¢

$3$ for $11$ ¢

每 $5$ 个 $18$ ¢

$5$ for $18$ ¢

每 $11$ 个 $40$ ¢

$11$ for $40$ ¢

每 $13$ 个 $50$ ¢

$13$ for $50$ ¢

答案：B

知识点：unit price weighted average break-even

难度评级：1210

小提示：

每次等量购买时都取 $15$ 个橙子，使两种报价都能整除

Use $15$ oranges in each equal-sized purchase so that both quoted rates divide evenly

大提示：

将 $30$ 个橙子的总成本与各个拟定售价比较

Compare the total cost of $30$ oranges with each proposed selling rate

解答：

假设他按每种价格各买 $15$ 个橙子。前 $15$ 个花费 $50$ ¢，后 $15$ 个花费 $60$ ¢，总计 $110$ ¢。因此 $30$ 个橙子必须卖 $110$ ¢，这等价于每 $3$ 个卖 $11$ ¢。

因此，正确答案是 B。

Suppose he buys $15$ oranges at each rate. The first $15$ cost $50$ ¢ and the second $15$ cost $60$ ¢, for $110$ ¢ total. Thus $30$ oranges must sell for $110$ ¢, which is equivalent to $3$ for $11$ ¢.

Therefore, the correct answer is B.

1955 AMC 12 第 6 题

答案：B

难度评级：1210

小提示：

大提示：

解答：

其他年份的第 6 题