A set of n positive numbers. Find the largest possible value of n.

Sorry I'm new to the forums and I'm not sure if this belongs here but some help on this one would be greatly appreciated. Thanks in advance.

The average of some set of n positive numbers is 60. After removing one of the numbers, the average of the remaining numbers is 70. What is the largest possible value of n?

Re: A set of n positive numbers. Find the largest possible value of n.

We have:

$\displaystyle \frac{x_1+x_2+... +x_{n-1}+x_{n}}{n}=60$ [1]

And

$\displaystyle \frac{x_1+x_2+... +x_{n-1}}{n-1}=70$

$\displaystyle x_1+x_2+... +x_{n-1}=70(n-1)$

Note that I removed x_n you could remove some x_i

now substitute in [1]:

you get

$\displaystyle 70(n-1) + x_n = 60n$

$\displaystyle x_n = 70 -10n$

so n < 7....