Question

一位演讲者在座无虚席的礼堂中演讲了六十分钟。听众中有百分之二十听完了全程，百分之十从头睡到尾。其余听众中，一半听了演讲的三分之一，另一半听了三分之二。听众平均听了多少分钟的演讲？

A speaker talked for sixty minutes to a full auditorium. Twenty percent of the audience heard the entire talk and ten percent slept through the entire talk. Half of the remainder heard one third of the talk and the other half heard two thirds of the talk. What was the average number of minutes of the talk heard by members of the audience?

$24$

$27$

$30$

$33$

$36$

答案：D

知识点：weighted averages percentages

难度评级：1180

小提示：

其余听众分成的两半各占全体听众的 $35\%$

The two halves of the remainder are each $35\%$ of the audience

大提示：

用相应的听众比例对听讲时间 $60,0,20$ 和 $40$ 加权

Weight the heard times $60,0,20,$ and $40$ by their audience fractions

解答：

平均时间为 $0.20(60)+0.10(0)$ $+0.35(20)+0.35(40)$ $=12+7+14=33$ 分钟。所以正确答案是 D。

The average is $0.20(60)+0.10(0)$ $+0.35(20)+0.35(40)$ $=12+7+14=33$ minutes. Thus D is correct.

1998 AMC 12 第 9 题

答案：D

难度评级：1180

小提示：

大提示：

解答：

其他年份的第 9 题