Question 251846
$1000 to the first born and 1/10 of what then remains,
 then $2000 to the second born and 1/10 of what then 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? 
:
let a = original amt to be divided among his children:
:
1sh. 1000 + .1(a-1000) = (1000 + .1a - 100)
(.1a + 900) = 1st child amt
: 
Subtract that from original amt:
a - (900+.1a) = (.9a - 900)
:
2sh. 2000 + .1[(.9a-900)-2000] = 2000 + .1(.9a-2900) = (2000 + .09a - 290)
(.09a + 1710) = 2nd child amt
;
It says the shares are equal, therefore we can find a:
1st child sh = 2nd child sh
.1a + 900 = .09a + 1710
.1a - .09a = 1710 - 900
.01a = 810
a = {{{810/.01}}}
a = $81,000; original amt to be divided
:
Find the share given to the 1st child using the equation
1sh = .1a + 900
1sh = .1(81000) + 900
1sh = 8100 + 900
1sh = $9000 amt to 1st child
:
Check to see if the 2nd child equation yields the same amt
2sh = .09a + 1710
2sh = .09(81000) + 1710
2sh = 7290 + 1710 
2sh = $9000 amt to 2nd child, so we are on the right track
:
It asks how many children are there
{{{81000/9000}}} = 9 children each getting 9000