# A father's will

• Mar 27th 2007, 07:13 AM
DivideBy0
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? :/
• Mar 27th 2007, 09:59 AM
earboth
Quote:

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