# Percent help

• Mar 25th 2014, 07:04 AM
Trolo
Percent help
There is 2 positive numbers
1 number is p% of the other

How many percent is those numbers geometric mean from arithmetic mean?

Answer is (20√(10) / p+100) %

How to get there? Been struggling with this so long. Its high school year 12 math.
Sorry for my bad english. (also for bad title, i dont know English definition for that)
• Mar 25th 2014, 08:35 AM
romsek
Re: Percent help
Quote:

Originally Posted by Trolo
There is 2 positive numbers
1 number is p% of the other

How many percent is those numbers geometric mean from arithmetic mean?

Answer is (20√(10) / p+100) %

How to get there? Been struggling with this so long. Its high school year 12 math.
Sorry for my bad english. (also for bad title, i dont know English definition for that)

you have two numbers $x$ and $y=\dfrac{px}{100}$

The arithmetic mean is $\dfrac{x+y}{2}=\dfrac{100x+px}{2\cdot 100}=\dfrac{(100+p)x}{200}$

The geometric mean is

$\sqrt{xy}=\sqrt{\dfrac{px^2}{100}}=\dfrac{x\sqrt{ p}}{10}$

I don't really know how to interpret your actual question, but given these two means you can figure out the ratio you are after.
• Mar 25th 2014, 11:26 AM
Trolo
Re: Percent help
Yea got the ratio! Thanks :)