Question

The average (arithmetic mean) length per film for a group of 21 films is t minutes. If a film that runs for 66 minutes is removed from the group and replaced by one that runs for 52 minutes, what is the average length per film, in minutes, for the new group of films, in terms of t ?

Answer 1

`t-(2)/(3)`

Explanation:

The average (arithmetic mean) length per film for a group of 21 films is t minutes

`Average = \frac{\text{Sum of minutes of films}}{\text{No. of films}}`

`t = \frac{\text{Sum of minutes of films}}{21}`

`21t =\text{Sum of minutes of films}`

A film that runs for 66 minutes is removed from the group and replaced by one that runs for 52 minutes

So,
`\text{New sum} = 21t-66+52=21t-14`

`\text{New Average} = \frac{\text{New sum}}{\text{No. of films}}`

`\text{New Average} = (21t-14)/(21)`

`\text{New Average} = t-(2)/(3)`

Hence the average length per film, in minutes, for the new group of films, in terms of t is
`t-(2)/(3)`