In his will Ethan left all his money to his children in the following manner:

- $1000 to the first born and one tenth of what then remains, then:
- $2000 to the second born and one tenth of what then remains, then:
- $3000 to the third born and one tenth of what then remains, and so on.....

When this is done each child had the same amount.

How many children were there?

I found the algebra a little easier with two variables.

Let p = each child's payment

T = total inheritance

Then, for the first child, p = 1000 + (T- 1000)/10

for the second child, p = 2000 + (T - p - 2000)/10

Subtracting equation 1 from 2 gives

0 = 1000 + (-p - 1000)/10

p + 1000 = 10,000

p = 9,000

So T = 81,000

Number of children = 81,000/9,000 = 9

*Edited on ***February 14, 2014, 5:51 pm**