Math  Algebra
posted by Anonymous on .
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 remains, and so on.
When this was done, each child had the same amount. How many children were there?
How would you solve this problem? This would be easy if it stated the total amount of money _
Answer: 9

F=1000+ 1/10 (A1000)
S=2000 + 1/10 (9/10(a1000) 2000)
T=3000 + 1/10 (9/10(a100020003000)
subtract the first from the second equation.
SF=20001000 + 9/100 (a1000)1/10(a1000)  200
0= 1000+a(.09 .1) 90 +100 200
0= 820 .01a
a=82,000 dollars.
Now the first kid got 1000+ 1/10 (81000) or 9,100 dollars.
Since they all got the same, the number of kids has to be 82000/9,1000 or nine kids. Of course, there was some change left over at the end. 
Could you show me a step by step on how to distribute the second child?
"S=2000 + 1/10 (9/10(a1000) 2000) "
I don't know how to properly distribute "9/10(a1000) 2000)" 
I know F = (9000 + x) / 10

were did you get 9/10 from