# Average age

The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?

Result

n =  15

#### Solution:

$s / n=n \ \\ s=n^2 \ \\ (s-29)/(n-1)=n-1 \ \\ n^2 - 29=(n-1)^2 \ \\ n^2 - 29=n^2 -2n + 1 \ \\ -29=-2n + 1 \ \\ 2n=30 \ \\ n=30/2=15$

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