smc

Question

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?

Accepted Answer

Assume that there are 100 people in the audience. 20 people heard 60 minutes of the talk, for a total of 20 60 = 1200 minutes heard. 10 people heard 0 minutes. 702 = 35 people heard 20 minutes of the talk, for a total of 35 20 = 700 minutes. 35 people heard 40 minutes of the talk, for a total of 1400 minutes. Altogether, there were 1200 + 0 + 700 + 1400 = 3300 minutes heard among 100 people. Thus, the average is 3300100 = 33 minutes, and the answer is 33.