1. ## mean

The mean of a set of numbers is 20. If one number is increased by 360, the mean increased to 40. How many numbers are in the set?

use no algebra.

2. $\displaystyle \frac{a_1+a_2+\dots +a_n}n+40=\frac{a_1+a_2+\dots +a_n+360}n \rightarrow 40=\frac {360}n\rightarrow \boxed{n=9}$.

3. I am not allowed to use any algebra.

4. Originally Posted by nancymcwilliams
The mean of a set of numbers is 20. If one number is increased by 360, the mean increased to 40. How many numbers are in the set?

use no algebra.
$\displaystyle 20 = \frac{\sum x_i}{n}$

$\displaystyle 40 = \frac{\left(\sum x_i\right) + 360}{n} = \frac{\sum x_i}{n} + \frac{360}{n} = 20 + \frac{360}{n}$

$\displaystyle \Rightarrow 20 = \frac{360}{n} \Rightarrow n = 18$.

5. Originally Posted by nancymcwilliams
I am not allowed to use any algebra.
Then just give the answer of 18 and say it came to you in a dream.

Fer cryin' out loud ...... I don't see how it can be done without some level of algebra being involved. Just say it's obvious that n = 360/20 - that way you're only using arithmetic.