Classroom And Averages

Algebra Level 2

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?

The answer is 19.

1 solution

Rishabh Jain
Mar 20, 2016

Let the average age of students be $x$ . This means that they are also $x$ in number which means sum of their ages $=x\times x=x^2$ . After teachers enter the room new sum of ages $=x^2+35+45=x^2+80$ and now there are $x+2$ people. Hence $\dfrac{x^2+80}{x+2}=x+2\\\implies x^2+80=(x+2)^2\\\implies \boxed{x=19}$

Which books did you refer for Physics and Chemistry in class 11? It's easy to communicate with you because as soon as I click discuss solutions after solving I see you.

Kushagra Sahni - 5 years, 2 months ago

Rasnick Halliday, HC Verma, Irrodov, McMurray,.... Many are in the list but what's the reason for your question?? :-)

Rishabh Jain - 5 years, 2 months ago

I am also preparing for JEE. That's why I was asking, I have HC Verma already

Kushagra Sahni - 5 years, 2 months ago

@Kushagra Sahni – Having learnt so much on brilliant you would definitely get some advantage in JEE..... :-)

Rishabh Jain - 5 years, 2 months ago

@Rishabh Jain – Thanks for that. I have a dream to become an IIT engineer and make new machines and solve the many environmental problems earth is facing.

Kushagra Sahni - 5 years, 2 months ago

@Kushagra Sahni – $\textbf{Brilliant}$ thought !!

Rishabh Jain - 5 years, 2 months ago

Classroom And Averages

The answer is 19.

1 solution

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