SOLUTION: 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 wh

Question 251846: 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 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?
a) 6 b) 7 c) 8 d) 9 e) none of these
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
$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 =
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
= 9 children each getting 9000
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