# Math Help - A father's will

1. ## A father's will

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? :/ 2. 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