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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 ?

Explanation	Calculations	Help
$We translate "the average length per film is t minutes" into an equation for the total length of the group of 21 films.$	$21 t = total length of the group of 21 films$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We subtract 66 minutes for the "removed" film and add 52 minutes for the "replaced by" film to find the new total length.$	$21 t - 66 + 52 = 21 t - 14 21 t - 14 = new total length of the group$	Theory & Tactics Method Card TRANS1-D Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We divide the new total length by 21 films to get the new average length per film.$	$\frac{21 t - 14}{21} = new average length per film$
$We simplify the fraction by separating the terms and reducing.$	$\frac{21 t - 14}{21} = \frac{21 t}{21} - \frac{14}{21} = t - \frac{14}{21} = t - \frac{2}{3}$

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t - \frac{2}{3}

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 ?

Explanation	Calculations	Help
$We translate "the average length per film is t minutes" into an equation for the total length of the group of 21 films.$	$21 t = total length of the group of 21 films$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We subtract 66 minutes for the "removed" film and add 52 minutes for the "replaced by" film to find the new total length.$	$21 t - 66 + 52 = 21 t - 14 21 t - 14 = new total length of the group$	Theory & Tactics Method Card TRANS1-D Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We divide the new total length by 21 films to get the new average length per film.$	$\frac{21 t - 14}{21} = new average length per film$
$We simplify the fraction by separating the terms and reducing.$	$\frac{21 t - 14}{21} = \frac{21 t}{21} - \frac{14}{21} = t - \frac{14}{21} = t - \frac{2}{3}$

Scroll horizontally to view all columns

t - \frac{2}{3}