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There are a certain number of students in a classroom. The average age of the students is equal to the number of students in the room.

Two professors that are respectively 35 and 45 years old enter the classroom. The average age of the people in the room is again equal to the number of people in the room.

How many students are in the room?

 Jan 18, 2021
 #1
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Call the  average  age  of the rooom before the  ptofessors enter the room, A

 

So......the total ages  of  the students  is number of studemts * average age  =     A*A  = A^2

 

So   when the professors enter the room we have that

 

[ A*A +  35 + 45 ]

______________  =    A + 2          cross-multiply

     A +  2

 

A^2  +  80  =  (A + 2) (A + 2)

 

A^2 + 80  =  A^2  + 4A + 4

 

80  =  4A  +  4

 

76 =  4A

 

19 =  A =  students in the room

 

Check....note that after the professors enter,  the number of people in the room =

 

(19^2  + 80) /( 19 + 2)  =   441/ 21  =  21

 

 

cool cool cool

 Jan 18, 2021

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