Originally Posted by

**DivideBy0** **A father in his will left all his money to his children in the following manner:**

**$1000 to the first born and 1/10 of what then remains,**

**then $2000 to the second born and 1/10 of what remains,**

**then $3000 to the third born and 1/10 of what then remains, and so on.**

**When this was done each child had the same amount. How many children were there?**

Which way is fastest and easiest? :/

Hi,

I don't know if my way is the easiest. I only did some plausible considerations and a final trial and error - and had success:

let x be the total amount of money

let n be the number of children

Then every child gets x/n

The first one gets:

$1000 + 1/10*(x -$1000) = x/n

$900 + 1/10*x = x/n

$900 = x*(1/n - 1/10)

x = $900 / (1/n - 1/10)

And now starts the guessing: The denominator cann't be negative that means the greatest number for n could be 9. So I took n = 9. That means x = $81,000. Now I checked the money each child will get:

Code:

child gets remains
------------------------------------
1 $1000 + $8000 $72,000
2 $2000 + $7000 $63,000
3 $3000 + $6000 $54,000
4 $4000 + $5000 $45,000
:
:

So every child gets the same amount of money

EB