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?
Let x be the amount to be divided.
Consider the first two children:
1000 + (x-1000)/10 = 2000 + (x - 3000 - (x-1000)/10)/10
10000 + (x-1000) = 20000 + x - 3000 - (x-1000)/10
100000 + 10x - 10000 = 200000 + 10x - 30000 - x + 1000
90000 = 170000 - x + 1000
x = 170000 - 90000 + 1000 = 81000 ; this is the amount to be divided
1000 + (x-1000)/10 = 9000 ; this is the amount per child, as it's what the first child gets
$81000 / ($9000/child) = 9 children
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Posted by Charlie
on 2014-02-13 12:17:07 |
solution
