Can you calculate the original average of some numbers by knowing how the average changes when you add numbers to it?
For example:
Let's say we have a class of some old students (we don't know their age or the average or the number of them). Then we are told that if we add the age of e.g. Dan, 16 to the ages of the students, the average age drops by 10 years, and then when we add the age of Michael, 12 to the new average, it drops by another 8 years. Can we just from this information calculate the average age of just the students?
Thanks for even reading this post.
Response to John Hughes:
I already tried doing this, but I got stuck at the point where you are supposed to do something with the things you've just written down. The things that I had written down that I thought I could get the answer from were:
$u-u'=S/N-(S+16)/(N+1)=10$
and
$u-u''=S/N-(S+28)/(N+2)=18$
I don't even know if this is what I was supposed to figure out.
How I figured it out:
After doing what John advised me to do I came up with this.
$S=10N^2+26N$
$2S=18N^2+64N$
In the first one, I divided both sides by N and in the second one, I divided both sides by 2 and by N. And this is what I got:
$S/N=10N+26$
$S/N=9N+32$
It seems pretty obvious that you should then put these equations together because they both equal $S/N$. Just like this:
$9N+32=10N+26$
and when you edit the equation
$6=N$
So now when you know what N equals you can plug it in another equation.
$S=10*6^2+26*6$
$S=516$
$u=S/N=516/6=86$
And that means the original average age is 86. Thanks for the help!